What is the sum of first eight terms of the series 1-(1)/(2)+(1)/(4)-(1)/(8)+ ?

Correct answer: C. (85)/(128) 1-(1)/(2)+(1)/(4)-(1)/(8)+ Sum of first ' n ' terms of G.P. S_n=1 · ((1-(-(1)/(2))^8))/(1-(-(1)/(2)))=(1-(1)/(256))/(1+(1)/(2))=((255)/(256))/((3)/(2))=(85)/(128) .

NDA 2012

Exam: NDA
Year: 2012
Subject: Mathematics
Chapter: Sequences and Series

NDA 2012 · Mathematics · Sequences and Series

What is the sum of first eight terms of the series...

What is the sum of first eight terms of the series

1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\ldots \ldots ?

Options

A $\frac{89}{128}$
B $\frac{57}{384}$
C $\frac{85}{128}$
DNone of the above

Correct answer

C. $\frac{85}{128}$

Step-by-step solution

1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\ldots \ldots \ldots

Sum of first '

n

' terms of G.P.

S_n=1 \cdot \frac{\left(1-\left(-\frac{1}{2}\right)^8\right)}{1-\left(-\frac{1}{2}\right)}=\frac{1-\frac{1}{256}}{1+\frac{1}{2}}=\frac{\frac{255}{256}}{\frac{3}{2}}=\frac{85}{128}

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