1.
fn(x)=min(xnn!,(1x)nn!)f_n(x)=\min(\frac{x^n}{n!},\frac{(1-x)^n}{n!}), x[0,1]x\in[0,1]. In=01fn(x)dxI_n=\int_0^1 f_n(x)dx. n=1In\sum_{n=1}^\infty I_n is