Question 3

The value of $$1+2^{2}+2^{3}+2^{4}+---+2^{9}$$ is __________.

Solution

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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