Question

Use mathematical induction to prove the statement is true for all positive integers n.

8 + 16 + 24 + ... + 8n = 4n(n + 1)

Answer 1

Let \(S_n = 8+16+24+\cdots+8n = 4n(n+1)\)

Check if \(S_1\) is true, then assume that \(S_k\) is true, show that \(S_{k+1} = S_{k}+8(k+1)\) is also true.