The sum of 10 terms of the series 3 1 2 × 2 2 + 5 2 2 × 3 2 + 7 3 2 × 4 2 + … is :

Step-by-step solution

Given that 3 1 2 × 2 2 + 5 2 2 × 3 2 + 7 3 2 × 4 2 + … Here 3 , 5 , 7 , - - - - ∈ A . P First term a   =   3   &   Common difference d   = 2 ,   t r   =   a   +   r - 1 d   =   3   +   r - 1 2   =   2 r + 1 = ∑ r = 1 10 ( 2 r + 1 ) r 2 · ( r + 1 ) 2 = ∑ r = 1 10 r 2 + 2 r + 1 - r 2 r 2 · ( r + 1 ) 2 = ∑ r = 1 10 ( r + 1 ) 2 - r 2 r 2 · ( r + 1 ) 2 = ∑ r = 1 10 1 r 2 -