Question

1²+1+2²+2+3²+3+--------------------+n²+n=​

Answer 1

Step-by-step explanation:

$( {1}^{2} + {2}^{2} + {3}^{2} + ...... + {n}^{2} ) + (1 + 2 + 3 + ....... + n) \\ As we know that, \\ {1}^{2} + {2}^{2} + {3 + ... + {n}^{2} } = \frac{n(n + 1)(2n + 1}{6} \\ 1 + 2 + 3 + ...... + n = \frac{n(n + 1)}{2} \\ now \\ = \frac{n(n + 1)(2n + 1)}{6} + \frac{n(n + 1)}{2} \\ \frac{n(n + 1)}{2}( \frac{2n + 1}{3} + 1) \\ = \frac{n(n + 1)}{2} ( \frac{2n + 4}{3}) \\ = \frac{n(n + 1)}{2}( \frac{2(n + 2)}{3} \\ = \frac{n(n + 1)(n + 2)}{3}$

Hope it helps you......

Answer 2

Step-by-step explanation:

See the above attachment.