Roboguru

Suku  dari uraian bentuk  adalah ....

Suku begin mathsize 14px style ke minus 6 end style dari uraian bentuk begin mathsize 14px style open parentheses a plus b close parentheses to the power of 10 end style adalah ....

  1. ...undefined 

  2. ...undefined 

Jawaban:

Secara umum rumus Binomial Newton dapat dinyatakan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses a plus b close parentheses to the power of n end cell equals cell sum from r equals 0 to n of space C open parentheses n comma r close parentheses times a to the power of n minus r end exponent times b to the power of r end cell row blank equals cell C open parentheses n comma 0 close parentheses times a to the power of n plus C open parentheses n comma 1 close parentheses times a to the power of n minus 1 end exponent times b to the power of 1 plus... plus C open parentheses n comma n close parentheses times b to the power of n end cell end table end style 

Berdasarkan bentuk tersebut dapat dilihat bahwa suku begin mathsize 14px style ke minus k end style dari bentuk tersebut diperoleh jika begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank r end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank k end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 1 end table end style. Sehingga dapat ditentukan suku begin mathsize 14px style ke minus 6 end style dari uraian bentuk begin mathsize 14px style open parentheses a plus b close parentheses to the power of 10 end style sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell C open parentheses n comma r close parentheses times a to the power of n minus r end exponent times b to the power of r end cell equals cell C open parentheses 10 comma 5 close parentheses times a to the power of 10 minus 5 end exponent times b to the power of 5 end cell row blank equals cell fraction numerator 10 factorial over denominator open parentheses 10 minus 5 close parentheses factorial 5 factorial end fraction a to the power of 5 times b to the power of 5 end cell row blank equals cell fraction numerator 10 cross times 9 cross times 8 cross times 7 cross times 6 cross times 5 factorial over denominator 5 cross times 4 cross times 3 cross times 2 cross times 1 cross times 5 factorial end fraction a to the power of 5 times b to the power of 5 end cell row blank equals cell 252 a to the power of 5 b to the power of 5 end cell end table end style  

Dengan demikian suku undefined dari undefined adalah begin mathsize 14px style 252 a to the power of 5 b to the power of 5 end style.

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