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Evaluate underset(nrarroo)(lim)sum(k=1)^...

Evaluate `underset(nrarroo)(lim)sum_(k=1)^(n)(1)/(2^(k))` and

Text Solution

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When the first few terms, `(1)/(2)+(1)/(4)+(1)/(8)+…,` are listed, it can be seen that `t_(1)=(1)/(2)` and the common ratio `r=(1)/(2)`. Therefore,
`S=((1)/(2))/(1-(1)/(2))=1`
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