Question

the sequence of natural numbers is divided into groups as follow (1);(2,3);(4,5,6);(7,8,9,10) and so on.Find the sum upto the 'k'group

Answer 1

As the u know the last term in the K group is K(K+1)/2
the sum of terms till is given by
$\frac{ \frac{k(k+1)}{2}(\frac{k(k+1)}{2}+1) }{2}= \frac{\frac{k(k+1)}{2}\frac{k(k+1)+2}{2}}{2}$
$= \frac{(k^2+k)^2+2(k^2+k)}{8}= \frac{k^4+k^2+2k^3+2k^2+2k}{8}= \frac{k^4+2k^3+3k^2+2k}{8}$