# Answer to Question #5795 in Algebra for nitish bindal

Question #5795

1 -1/8 + 1.3/8.16 - 1.3.5/8.16.24 ...........

ans. 2/5^1/2

ans. 2/5^1/2

Expert's answer

Calculate.

Please show your work

1 - 1/8 + 1.3/8.16 - 1.3.5/8.16.24 ...........

ans. 2/5^1/2

1 - 1/8 + 1.3/8.16 - 1.3.5/8.16.24 ... =& 1 -& (1/2)(1/4) + (1.3/2!.2.2)(1/4)^2- (1.3.5/3!.2.2.2)(1/4)^3 + ... ,

which is of the form

1 - nx + [n.(n+1)/2!]x^2 - [n.(n+1)(n+2)/3!]x^3 ... ,

where n=1/2 and x=1/4, and

1 - nx + [n.(n+1)/2!]x^2 - [n.(n+1)(n+2)/3!]x^3 ... = (1+x)^(-n).

Therefore, 1 - 1/8 + 1.3/8.16 - 1.3.5/8.16.24 ... = (1+1/4)^(-1/2) = (5/2)^(-1/2) = (2/5)^(1/2).

Please show your work

1 - 1/8 + 1.3/8.16 - 1.3.5/8.16.24 ...........

ans. 2/5^1/2

1 - 1/8 + 1.3/8.16 - 1.3.5/8.16.24 ... =& 1 -& (1/2)(1/4) + (1.3/2!.2.2)(1/4)^2- (1.3.5/3!.2.2.2)(1/4)^3 + ... ,

which is of the form

1 - nx + [n.(n+1)/2!]x^2 - [n.(n+1)(n+2)/3!]x^3 ... ,

where n=1/2 and x=1/4, and

1 - nx + [n.(n+1)/2!]x^2 - [n.(n+1)(n+2)/3!]x^3 ... = (1+x)^(-n).

Therefore, 1 - 1/8 + 1.3/8.16 - 1.3.5/8.16.24 ... = (1+1/4)^(-1/2) = (5/2)^(-1/2) = (2/5)^(1/2).

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