Use induction to prove the following formula is true for all integers n where n greaterthanorequalto 1. 1 + 4 + 9 + .. + n^2 = n(n + 1)(2n + 1)/6

Answer with Step-by-step explanation:

Since we have given that

1+4+9+........................+n² =

We will show it using induction on n:

Let n = 1

L.H.S. :1 = R.H.S. :

So, P(n) is true for n = 1

Now, we suppose that P(n) is true for n = k.

Now, we will show that P(n) is true for n = k+1.

So, it L.H.S. becomes,

and R.H.S. becomes,

Consider, L.H.S.,

So, L.H.S. = R.H.S.

Hence, P(n) is true for all integers n.

step-by-step explanation:

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step-by-step explanation: