If _ n [ (1+ 1 n^2 ) (1+ 4 n^2 ) (1+ 9 n^2 ) (1+ n^2 n^2 ) ]^ 1 n = ae ^ b , then a+b=

Step-by-step solution

Let y= _ n [ (1+ 1 n^2 ) (1+ 4 n^2 ) (1+ n^2 n^2 ) ]^ 1 n aligned & y= _ n 1 n _ r=1 ^n [ (1+ r^2 n^2 ) ] & y= _ n 1 n _ r=1 ^n [1+ ( r n )^2 ] aligned y= ₀^1 (1+x^2 )= [ (1+x^2 ) x ]₀^1- ₀^1 2 x^2 1+x^2 d x aligned & = 2-2(x- x)= 2-2+ 2 & y=e^ 2-2+ 2 =a e^b aligned So, a =2, b=-2+ 2 a+b= 2 .