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

2) Deduce that:

$\displaystyle \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

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