Question

State whether the following proof (by mathematical induction) is true or false for the statement.

P(n): 1² + 2² + ... + n² =(n(n+1)(2n+1))/6

Answer 1

By the Principle of Mathematical induction, P(n) is true for n = 1,

Again for some k ≥ 1,

Now we prove that

Solution False

Since in the inductive step both the inductive hypothesis and what is to be proved are wrong.