# Math Help - Integration by parts, limits

1. ## Integration by parts, limits

1) Show that $\int_0^1 \ln (1+x) dx= -1 +\log 4$

2) Deduce that:

$\left(\left(1+\frac{1}{n}\right)\left(1+\frac{2}{n }\right)...\left(1+\frac{n}{n}\right)\right)^{\fra c{1}{n}} \rightarrow \frac{4}{e}\ as\ n \rightarrow \infty

$

2. To get 2, take logarithms and note that the LHS is a Riemann sum for the integral in 1.