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The value of 1 + 2^2 + 2^3 + 2^4 + ……+ ...

The value of `1 + 2^2 + 2^3 + 2^4 + ……+ 2^9` is ______

A

255

B

511

C

1021

D

2047

Text Solution

AI Generated Solution

To find the value of the expression \(1 + 2^2 + 2^3 + 2^4 + \ldots + 2^9\), we can recognize that the terms from \(2^2\) to \(2^9\) form a geometric progression (GP). Let's break down the solution step by step. ### Step 1: Identify the terms of the series The series can be rewritten as: \[ 1 + (2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 + 2^9) \] Here, we have the first term as \(1\) and the remaining terms form a GP starting from \(2^2\) to \(2^9\). ...
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