Problem

Find the sum of the series 1+2+4+8+16+...+1024

Answer

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Answer

Substituting a=1, r=2, and n=10 into the formula, we get S10=1(210−1)2−1=1024−1=1023.

Steps

Step 1 ：This is a geometric series with first term a=1 and common ratio r=2. The sum of the first n terms of a geometric series can be found using the formula Sn=a(rn−1)r−1. We need to find the value of n such that 2n=1024.

Step 2 ：Solving the equation 2n=1024, we get n=10.

Step 3 ：Substituting a=1, r=2, and n=10 into the formula, we get S10=1(210−1)2−1=1024−1=1023.

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