Question

1 + ( 1 + 2) + ( 1 + 2 + 3 ) + ........n terms, Find Sn​

Answer 1

Solution:-

$S_{n} = 1 + ( 1+ 2 ) + ( 1 + 2 + 3 ) + .......+ n terms$

$n^{th} \: term$

$T_{n} = 1 + 2 + 3 + ...... + n$

$T_{n} = submisation of n = \frac{n ( n + 1)}{2}$

so,

Sn = Σ Tn = (Σn^2 + n)/2

= 1/2 { 2n^2 + Σn}

Sn = 1/2 { n ( n + 1 )( n + 2 )}/6

Thank you....