If S (x)=(1+x)+2(1+x)^2+3(1+x)^3+ +60(1+x)⁶⁰, x 0 , and (60)^2 ~S (60)= a ( b )^ b + b , where a, b N , then (a+b) equal to ______

Step-by-step solution

aligned S(x)= & (1+x)+2(1+x)^2+3(1+x)^3+. .+60(1+x)⁶⁰ (1+x) S= & (1+x)^2+ . 59(1+x)⁶⁰+60(1+x)⁶¹ & -x S= (1+x)(1+x)⁶⁰-1 x -60(1+x)⁶¹ aligned Put x =60-60 ~S = 61 ((61)⁶⁰-1 ) 60 -60(61)⁶¹ on solving 3660