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Nilai n yang memenuhi  adalah...

Pertanyaan

Nilai n yang memenuhi size 14px sum from size 14px k size 14px equals size 14px 1 to size 14px n of size 14px left parenthesis size 14px 4 size 14px k size 14px plus size 14px 5 size 14px right parenthesis size 14px equals size 14px 774 adalah...

  1. 16

  2. 18

  3. 20

  4. 22

  5. 24

Pembahasan Video:

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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Terakhir diupdate 03 Mei 2021

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Pertanyaan yang serupa

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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Buktikan bahwa:

Pembahasan Soal:

begin mathsize 14px style sum from k equals 10 to 20 of left parenthesis k squared plus 20 k plus 103 right parenthesis plus sum from k equals 10 to n minus 11 of left parenthesis k squared plus 42 k plus 444 right parenthesis equals sum from k equals 10 plus 10 to 20 plus 10 of left parenthesis left parenthesis k minus 10 right parenthesis squared plus 20 left parenthesis k minus 10 right parenthesis plus 103 right parenthesis space space space space space space plus sum from k equals 10 plus 21 to n minus 11 plus 21 of left parenthesis left parenthesis k minus 21 right parenthesis squared plus 42 left parenthesis k minus 21 right parenthesis plus 444 right parenthesis equals sum from k equals 20 to 30 of left parenthesis k squared minus 20 k plus 100 plus 20 k minus 200 plus 103 right parenthesis space space space space space space plus sum from k equals 31 to n plus 10 of left parenthesis k squared minus 42 k plus 441 plus 42 k minus 882 plus 444 right parenthesis equals sum from k equals 20 to 30 of left parenthesis k squared plus 3 right parenthesis plus sum from k equals 31 to n plus 10 of left parenthesis k squared plus 3 right parenthesis equals sum from k equals 20 to n plus 10 of left parenthesis k squared plus 3 right parenthesis subscript left parenthesis Terbukti right parenthesis end subscript end style   

0

Roboguru

Notasi sigma yan gekuivalen dengan  adalah...

Pembahasan Soal:

begin mathsize 14px style sum from k equals 2 to 6 of open parentheses k squared plus 2 k close parentheses minus sum from k equals 5 to 9 of left parenthesis 3 k minus 5 right parenthesis equals sum from k equals 2 plus 1 to 6 plus 1 of open parentheses open parentheses k minus 1 close parentheses squared plus 2 k close parentheses minus sum from k equals 5 minus 2 to 9 minus 2 of left parenthesis 3 left parenthesis k plus 2 right parenthesis minus 5 right parenthesis equals sum from k equals 3 to 7 of open parentheses k squared minus 2 k plus 1 plus 2 k close parentheses minus sum from k equals 3 to 7 of left parenthesis 3 k plus 6 minus 5 right parenthesis equals sum from k equals 3 to 7 of open parentheses k squared plus 1 close parentheses minus sum from k equals 3 to 7 of left parenthesis 3 k plus 1 right parenthesis equals sum from k equals 3 to 7 of k squared minus 3 k equals sum from k equals 3 to 7 of k left parenthesis k minus 3 right parenthesis end style 

Jadi, jawaban yang tepat adalah C.

0

Roboguru

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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Notasi sigma yan gekuivalen dengan  adalah...

Pembahasan Soal:

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