Question

Prove that  1² + 2² + 3² + ………… + n² = (n(n + 1)(2n + 1))/6

Answer 1

Let P(n) : 1² + 2² + 3² + ………… + n² = (n(n + 1)(2n + 1))/6

Step 1: P(1) is true

when n = 1; L.H.S = 1² = 1

R.H.S = (1(1 + 1)(2 + 1))/6

∴ L.H.S = R.H.S 

∴ P(1) is true

step 2: Assume that P(m) is true

= R.H.S 

∴ P(m+1) is true 

Conclusion: P(1) is true 

⇒ P(m) is true 

⇒ P(m+1) is true 

∴ By principle of mathematical induction, the result is true for all natural numbers ‘n’.