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Find the sum of the grometric series 1+1...

Find the sum of the grometric series `1+1/2+1/4+1/8+...` to 12 terms.

Text Solution

Verified by Experts

Here `a=1, r=1/2 lt 1` and `n=12`.
Using the formula, `S_(n)=(a(1-r^(n)))/((1-r))`, we get
`S_(12)=(1xx{1-(1/2)^(n)})/((1-1/2))=((1-1/2^(12)))/((1/2))=((2^(12)-1))/2^(11)=4095/2048`.
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