Use mathimatical Induction to prove that 1²+2²+3²+.......n²= n(n+1)(2n+1) divided by 6
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First we need to show the result is true for smallest value of n, in this case n = 0/
When n =0 the left side has only one term n2 = 0
The right side is
The second step is to show the statement is true for n = k, k+1 and so on.
Suppose, that statement is true for n = K.
12 + 22 + 32 + … + k2 =
We need to prove, that statement is true fof n = k+1
12 + 22 + 32 + … + (k+1)2 =
12 + 22 + 32 + … +k2 + (k+1)2 =
We know, that
12 + 22 + 32 + … +k2 =
= RHS hence proved