If u(n)= ₀^ 2 (1+ t)^n 2 t d t, n N , then u(4)=

Step-by-step solution

Given u(n)= ₀^ / 2 (1+ t)^n 2 t d t u ( n )=2 ₀^ / 2 (1+ t )^ n t t d t Let 1+ t = u tdt = du aligned & =2 ₁^2 u^n(u-1) d u & =2 ₁^2 (u^ n+1 -u^n ) d u=2 ( u^ n+2 n+2 - u^ n+1 n+1 )₁^2 & u(4)=2 ( u^6 6 - u^5 5 )₁^2 & =2 ( 2^6 6 - 2^5 5 )-2 ( 1 6 - 1 5 ) & = 128 15 + 1 15 = 129 15 aligned