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Diketahui . Nilai dari  adalah...

Pertanyaan

Diketahui size 14px sum from size 14px n size 14px equals size 14px 6 to size 14px 25 of size 14px pi size 14px equals size 14px 10. Nilai dari size 14px sum from size 14px n size 14px equals size 14px 6 to size 14px 25 of open parentheses 2 plus pi close parentheses adalah... 

  1. 50

  2. 60

  3. 70

  4. 80

  5. 90

Pembahasan Video:

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sum from n equals 6 to 25 of left parenthesis 2 plus p i right parenthesis end cell equals cell sum from n equals 6 to 25 of 2 plus sum from n equals 6 to 25 of p i end cell row blank equals cell left parenthesis 25 minus 6 plus 1 right parenthesis cross times 2 plus 10 end cell row blank equals cell 20 cross times 2 plus 10 end cell row blank equals cell 40 plus 10 end cell row blank equals 50 end table end style 

Jadi, jawaban yang tepat adalah A.

Pembahasan terverifikasi oleh Roboguru

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Terakhir diupdate 03 Mei 2021

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Notasi sigma yang ekuivalen dengan  adalah...

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sum from k equals 5 to 9 of open parentheses 2 k minus 5 close parentheses squared end cell equals cell sum from k equals 5 minus 4 to 9 minus 4 of open parentheses 2 open parentheses k plus 4 close parentheses minus 5 close parentheses squared end cell row blank equals cell sum from k equals 1 to 5 of open parentheses 2 k plus 8 minus 5 close parentheses squared end cell row blank equals cell sum from k equals 1 to 5 of open parentheses 2 k plus 3 close parentheses squared end cell row blank equals cell sum from k equals 1 to 5 of open parentheses 4 k squared plus 12 k plus 9 close parentheses end cell row blank equals cell sum from k equals 1 to 5 of 4 k squared plus sum from k equals 1 to 5 of left parenthesis 12 k plus 9 right parenthesis end cell row blank equals cell 4 sum from k equals 1 to 5 of k squared plus sum from k equals 1 to 5 of 3 left parenthesis 4 k plus 3 right parenthesis end cell row blank equals cell 4 sum from k equals 1 to 5 of k squared plus 3 sum from k equals 1 to 5 of left parenthesis 4 k plus 3 right parenthesis end cell end table end style 

Jadi, jawaban yang tepat adalah D.

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Nilai n yang memenuhi  adalah...

Pembahasan Soal:

begin mathsize 14px style sum from k equals 1 to n of left parenthesis 4 k plus 5 right parenthesis equals 774 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis 4 cross times 1 plus 5 right parenthesis plus left parenthesis 4 cross times 2 plus 5 right parenthesis plus left parenthesis 4 cross times 3 plus 5 right parenthesis plus... plus left parenthesis 4 cross times n plus 5 right parenthesis end cell equals 774 row cell 9 plus 13 plus 17 plus 21 plus... plus left parenthesis 4 n plus 5 right parenthesis end cell equals 774 end table end style 

Notasi sigma di atas merupakan deret aritmatika dengan begin mathsize 14px style a equals 9 comma space U subscript n equals left parenthesis 4 n plus 5 right parenthesis comma space dan space S subscript n equals 774 end style

Maka diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell S subscript n end cell equals cell n over 2 open parentheses a plus U subscript n close parentheses end cell row 774 equals cell n over 2 left parenthesis 9 plus left parenthesis 4 n plus 5 right parenthesis right parenthesis end cell row 774 equals cell n over 2 left parenthesis 14 plus 4 n right parenthesis end cell row 774 equals cell n left parenthesis 7 plus 2 n right parenthesis end cell row 774 equals cell 7 n plus 2 n squared end cell row cell 2 n squared plus 7 n minus 774 end cell equals 0 row cell left parenthesis n minus 18 right parenthesis left parenthesis n plus 43 right parenthesis end cell equals 0 row blank blank blank end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis n minus 18 right parenthesis end cell equals cell 0 space space space a t a u space left parenthesis 2 n plus 43 right parenthesis equals 0 end cell row n equals cell 18 space a t a u space space space space space space space space space space space space space space n equals negative 43 over 2 subscript left parenthesis tidak space memenuhi right parenthesis end subscript end cell end table end style 

Jadi, jawaban yang tepat adalah B. 

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Buktikan bahwa:

Pembahasan Soal:

begin mathsize 14px style sum from i equals 1 to 48 of left parenthesis 2 i plus 5 right parenthesis plus sum from i equals 60 to n plus 9 of left parenthesis 2 i minus 17 right parenthesis equals sum from i equals 1 plus 2 to 48 plus 2 of left parenthesis 2 left parenthesis i minus 2 right parenthesis plus 5 right parenthesis plus sum from i equals 60 minus 9 to n plus 9 minus 9 of left parenthesis 2 left parenthesis i plus 9 right parenthesis minus 17 right parenthesis equals sum from i equals 3 to 50 of left parenthesis 2 i minus 4 plus 5 right parenthesis plus sum from i equals 51 to n of left parenthesis 2 i plus 18 minus 17 right parenthesis equals sum from i equals 3 to 50 of left parenthesis 2 i plus 1 right parenthesis plus sum from i equals 51 to n of left parenthesis 2 i plus 1 right parenthesis equals sum from i equals 3 to n of left parenthesis 2 i plus 1 right parenthesis subscript left parenthesis Terbukti right parenthesis end subscript end style  

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Diketahui . Nilai

Pembahasan Soal:

Dengan menggunakan konsep notasi sigma, diperoleh:

begin mathsize 14px style sum from k equals 21 to 100 of open parentheses a subscript k minus 20 end subscript plus 5 close parentheses plus sum from k equals 60 to 79 of open parentheses a subscript k plus 21 end subscript minus 5 close parentheses equals sum from k equals 21 minus 20 to 100 minus 20 of open parentheses a subscript k plus 20 minus 20 end subscript plus 5 close parentheses plus sum from k equals 60 plus 21 to 79 plus 21 of open parentheses a subscript k minus 21 plus 21 end subscript minus 5 close parentheses equals sum from k equals 1 to 80 of open parentheses a subscript k plus 5 close parentheses plus sum from k equals 81 to 100 of open parentheses a subscript k minus 5 close parentheses equals sum from k equals 1 to 80 of a subscript k plus sum from k equals 1 to 80 of 5 plus sum from k equals 81 to 100 of a subscript k minus sum from k equals 81 to 100 of 5 equals sum from k equals 1 to 100 of a subscript k plus left parenthesis 80 minus 1 plus 1 right parenthesis cross times 5 minus left parenthesis 100 minus 81 plus 1 right parenthesis cross times 5 equals 50 plus 80 cross times 5 minus 20 cross times 5 equals 50 plus 60 cross times 5 equals 50 plus 300 equals 350 end style 

Jadi, jawaban yang tepat adalah B.

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Nilai  =...

Pembahasan Soal:

begin mathsize 14px style sum from a equals 7 to 12 of open parentheses a squared plus 4 close parentheses minus sum from a equals 1 to 6 of open parentheses a squared plus 4 a minus 5 close parentheses equals sum from a equals 7 minus 6 to 12 minus 6 of open parentheses open parentheses a plus 6 close parentheses squared plus 4 close parentheses minus sum from a equals 1 to 6 of open parentheses a squared plus 4 a minus 5 close parentheses equals sum from a equals 1 to 6 of open parentheses a squared plus 12 a plus 36 plus 4 minus a squared minus 4 a plus 5 close parentheses equals sum from a equals 1 to 6 of left parenthesis 8 a plus 45 right parenthesis equals sum from a equals 1 to 6 of 8 a plus sum from a equals 1 to 6 of 45 equals 8 sum from a equals 1 to 6 of a plus sum from a equals 1 to 6 of 45 equals 8 left parenthesis 1 plus 2 plus 3 plus 4 plus 5 plus 6 right parenthesis plus 6 cross times 45 equals 8 cross times 21 plus 270 equals 168 plus 270 equals 438 end style 

Jadi, jawaban yang tepat adalah D.

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