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  4. The sum of 10 terms of GP (1/2)+(1/4)+(1/8)+ ldots ldots ldots ldots. is

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Q. The sum of 10 terms of GP $\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\ldots \ldots \ldots \ldots$. is

Sequences and Series

Solution:

$a =1 / 2$ and $r=1 / 2$
$\Rightarrow S _{10}=\frac{1}{2} \frac{\left(1-\frac{1}{2}\right)^{10}}{1-\frac{1}{2}}=\frac{2^{10}-1}{2^{10}}$