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

Question

Accepted Answer

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 (S_n = frac{a(r^n-1)}{r-1}). We need to find the value of (n) such that (2^n = 1024).Step:2 ：Solving the equation (2^n = 1024), we get (n = 10).Step:3 ：Substituting (a = 1), (r = 2), and (n = 10) into the formula, we get (S_{10} = frac{1(2^{10}-1)}{2-1} = 1024 - 1 = 1023).

Answer

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 (S_n = frac{a(r^n-1)}{r-1}). We need to find the value of (n) such that (2^n = 1024).Step: 2 ：Solving the equation (2^n = 1024), we get (n = 10).Step: 3 ：Substituting (a = 1), (r = 2), and (n = 10) into the formula, we get (S_{10} = frac{1(2^{10}-1)}{2-1} = 1024 - 1 = 1023).

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

Answer

Popular Problems