Mathematics, 30.07.2019 21:10 DwayneLeonard618
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
Answers: 3
![1+4+9+..+k^2+(k+1)^2\\\\=\dfrac{k(k+1)(2k+1)}{6}+(k+1)^2\\\\=k+1[\dfrac{k(2k+1)}{6}+(k+1)]\\\\=(k+1)[\dfrac{2k^2+k+6k+6}{6}]\\\\=(k+1)\dfrac{2k^2+7k+6}{6}]\\\\=(k+1)\dfrac{2k^2+4k+3k+6}{6}]\\\\=(k+1)[\dfrac{2k(k+2)+3(k+2)}{6}]\\\\=\dfrac{(k+1)(2k+3)(k+2)}{6}](/tpl/images/0151/9072/006f2.png)
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