Prove the following by the principle of mathematical induction: To prove: Prove that by the Mathematical Induction.

Question

Philoid · Accepted Answer

Let Assume P(n):1² + 2² + 3² + - - - + n² =

For n = 1

P(1): 1 =

1=1

= P(n) is true for n = 1

Let P(n) is true for n = k, so

P(k): 1² + 2² + 3² + - - - - - + k² =

Let’s check for P(n) = k + 1, So

P(k): 1² + 2² + 3² + - - - - - + k² + (k + 1)² =

= 1² + 2² + 3² + - - - - - + k² + (k + 1)²

=

Therefore, P(n) is true for n = k + 1

Hence, P(n) is true for all n∈N by PMI