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Diketahui penjumlahan 100 + 96 x + 92 x 2 + 88 x 3 + 84 x 4 + 80 x 5 + ... + 4 x 24 . Notasi sigma penjumlahan di atasadalah …

Diketahui penjumlahan .

Notasi sigma penjumlahan di atas adalah   

  1. begin mathsize 14px style sum from i equals 0 to 26 of left parenthesis 100 minus 4 i right parenthesis x to the power of i end style         

  2. begin mathsize 14px style sum from i equals 0 to 25 of left parenthesis 100 minus 4 i right parenthesis x to the power of i end style 

  3. begin mathsize 14px style sum from i equals 0 to 25 of left parenthesis 104 minus 4 i right parenthesis x to the power of i end style 

  4. begin mathsize 14px style sum from i equals 1 to 24 of left parenthesis 100 minus 4 i right parenthesis x to the power of i end style 

  5. begin mathsize 14px style sum from i equals 1 to 23 of left parenthesis 104 minus 4 i right parenthesis x to the power of i minus 1 end exponent end style 

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S. Yoga

Master Teacher

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Jawaban

notasi sigma dari adalah atau

notasi sigma dari begin mathsize 14px style 100 plus 96 x plus 92 x squared plus 88 x cubed plus 84 x to the power of 4 plus 80 x to the power of 5 plus... plus 4 x to the power of 24 end style adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sum from i equals 0 to 24 of left parenthesis 100 – 4 i right parenthesis x to the power of i end cell end table end style atau begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sum from i equals 1 to 25 of left parenthesis 104 – 4 i right parenthesis x to the power of i – 1 end exponent end cell end table end style 

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Pembahasan

Deret merupakan deret aritmetika yang memiliki suku pertama ,suku kedua dan suku terakhir . Beda deret: . Rumus suku ke- deret: Dengan demikian, deret dapat dituliskan dalam bentuk: Bentuk notasi sigma dengan batas bawah 0: Jadi, notasi sigma dari adalah atau

Deret begin mathsize 14px style 100 plus 96 plus 92 plus 88 plus 84 plus 80 plus... plus 4 end style merupakan deret aritmetika yang memiliki suku
pertama begin mathsize 14px style U subscript 1 equals a equals 100 end style, suku kedua begin mathsize 14px style U subscript 2 equals 96 end style dan suku terakhir begin mathsize 14px style U subscript n equals 4 end style. 

Beda deret:

begin mathsize 14px style b equals U subscript 2 – U subscript 1 equals 100 – 96 equals – 4 end style.

Rumus suku ke-begin mathsize 14px style n end style deret:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell U subscript n end cell equals cell a plus left parenthesis n – 1 right parenthesis b end cell row blank equals cell 100 plus left parenthesis n – 1 right parenthesis cross times left parenthesis – 4 right parenthesis end cell row blank equals cell 100 – 4 n plus 4 end cell row blank equals cell 104 – 4 n end cell end table end style  

Dengan demikian, deret begin mathsize 14px style 100 plus 96 x plus 92 x squared plus 88 x cubed plus 84 x to the power of 4 plus 80 x to the power of 5 plus... plus 4 x to the power of 24 end style dapat dituliskan dalam bentuk: 

begin mathsize 14px style 100 plus 96 x plus 92 x squared plus 88 x cubed plus 84 x to the power of 4 plus 80 x to the power of 5 plus... plus 4 x to the power of 24 equals left parenthesis 104 – 4 cross times 1 right parenthesis x to the power of 0 plus left parenthesis 104 – 4 cross times 2 right parenthesis x to the power of 1 plus left parenthesis 104 – 4 cross times 3 right parenthesis x squared space space space plus left parenthesis 104 – 4 cross times 4 right parenthesis x cubed plus left parenthesis 104 – 4 cross times 5 right parenthesis x to the power of 4 plus left parenthesis 104 – 4 cross times 6 right parenthesis x to the power of 5 space space space plus... plus left parenthesis 104 – 4 cross times 25 right parenthesis x to the power of 24 equals left parenthesis 104 – 4 cross times 1 right parenthesis x to the power of 1 – 1 end exponent space space space plus left parenthesis 104 – 4 cross times 2 right parenthesis x to the power of 2 – 1 end exponent plus left parenthesis 104 – 4 cross times 3 right parenthesis x to the power of 3 – 1 end exponent space space space plus left parenthesis 104 – 4 cross times 4 right parenthesis x to the power of 4 – 1 end exponent plus left parenthesis 104 – 4 cross times 5 right parenthesis x to the power of 5 – 1 end exponent space space plus left parenthesis 104 – 4 cross times 6 right parenthesis x to the power of 6 – 1 end exponent plus... plus left parenthesis 104 – 4 cross times 25 right parenthesis x to the power of 25 – 1 end exponent equals sum from i equals 1 to 25 of left parenthesis 104 – 4 i right parenthesis x to the power of i – 1 end exponent end style 

Bentuk notasi sigma dengan batas bawah 0:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sum from i equals 1 to 25 of left parenthesis 104 – 4 i right parenthesis x to the power of i – 1 end exponent end cell equals cell sum from i equals 1 minus 1 to 25 minus 1 of left parenthesis 104 – 4 left parenthesis i plus 1 right parenthesis right parenthesis x to the power of left parenthesis i plus 1 right parenthesis – 1 end exponent end cell row blank equals cell sum from i equals 0 to 24 of left parenthesis 100 – 4 i right parenthesis x to the power of i end cell end table end style 

Jadi, notasi sigma dari begin mathsize 14px style 100 plus 96 x plus 92 x squared plus 88 x cubed plus 84 x to the power of 4 plus 80 x to the power of 5 plus... plus 4 x to the power of 24 end style adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sum from i equals 0 to 24 of left parenthesis 100 – 4 i right parenthesis x to the power of i end cell end table end style atau begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sum from i equals 1 to 25 of left parenthesis 104 – 4 i right parenthesis x to the power of i – 1 end exponent end cell end table end style 

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