1. The value of $$1+2^{2}+2^{3}+2^{4}+---+2^{9}$$ is __________.
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By: anil on 05 May 2019 02.05 am
Expression : $$1+2^{2}+2^{3}+2^{4}+---+2^{9}$$ = $$(2^0+2^1+2^{2}+2^{3}+2^{4}+---+2^{9})-2$$ The above series is a geometric progression with first term, $$a=1$$ and common ratio, $$r=2$$ Number of terms, $$n=10$$ Sum of G.P. = $$frac{a(r^n-1)}{r-1}$$ = $$[frac{1(2^{10}-1)}{2-1}]-2$$ = $$1024-1-2=1021$$ => Ans - (C)
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