Question

Give me the solutions for all problems in principle of mathematical induction.plz pa

Answer 1

Using the principle of mathematical induction, prove that 

1² + 2² + 3² + ..... + n² = (1/6){n(n + 1)(2n + 1} for all n ∈ N. 

Solution: 

Let the given statement be P(n). Then, 

P(n): 1² + 2² + 3² + ..... +n² = (1/6){n(n + 1)(2n + 1)}. 

Putting n =1 in the given statement, we get 

LHS = 1² = 1 and RHS = (1/6) × 1 × 2 × (2 × 1 + 1) = 1. 

Therefore LHS = RHS. 

Thus, P(1) is true.