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Mathematics

If the sum of 1 + 2 + 22 + …….. + 2n - 1 is 255, find the value of n.

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Answer

Common ratio = 2.

Since, |r| > 1

⇒S=a(rn−1)(r−1)⇒255=1(2n−1)(2−1)⇒2n−1=255⇒2n=256⇒2n=28⇒n=8.\Rightarrow S = \dfrac{a(r^n - 1)}{(r - 1)} \\[1em] \Rightarrow 255 = \dfrac{1(2^n - 1)}{(2 - 1)} \\[1em] \Rightarrow 2^n - 1 = 255 \\[1em] \Rightarrow 2^n = 256 \\[1em] \Rightarrow 2^n = 2^8 \\[1em] \Rightarrow n = 8.

Hence, n = 8.

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