Question

prove that the mathematical induction for 1^2+2^2+3^2+.......+n^2= n(n+1) (n+2)/ 6​

Answer 1

Step-by-step explanation:

step 1 : Prove that P(1) is true when n= 1; L.H.S = 12 = 1 R.H.S = 1(1 + 1)(2 + 1)/6 = 2.3/6 = 1 ∴ L.H.S = R.H.S ∴ P(1) is true step 2: Assume that P(m) is true i.e., 12 + 22 + 32 + ………. + m2 = (n(m + 1)(2m + 1))/6……… (1) step 3: Prove that 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’.Read more on Sarthaks.com - https://www.sarthaks.com/598624/prove-by-mathematical-induction-1-2-2-2-3-2-n-2-n-n-1-2n-1-6-n-n?show=598638#a598638