SOLUTION: proof of
1+4+9+16+25+36+...+n^2=(n(n+1)(2*n+1))/6
plz answer me soon
Algebra.Com
Question 504679: proof of
1+4+9+16+25+36+...+n^2=(n(n+1)(2*n+1))/6
plz answer me soon
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
It is easy to prove via induction; but more difficult to derive the formula. To prove it by induction, note that the base case n = 1 holds. Assume it holds for n=k, e.g.
(2k+1)}{6})
. Then we want to show it works for k+1:
^2 = (1 + ... + k^2) + (k+1)^2 = \frac{k(k+1)(2k+1)}{6} + (k+1)^2)
(2k+1)}{6} + \frac{6(k+1)^2}{6} = \frac{(k+1)(k(2k+1) + 6(k+1))}{6})
(2k^2 + 7k + 6)}{6} = \frac{(k+1)(k+2)(2k+3)}{6})
which is what we would've gotten if we substituted k+1 into the formula. Hence the statement is true for all positive integers n.
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