Question

y = $\frac{1}{n}$ [(n + 1) (n + 2) …….2n]^1/n then$\underset{n \rightarrow \infty}{Lim}$y is equal to

• A. log$\frac{4}{e}$
• B. $\log\left( \frac{2}{e} \right)$
• C. $\frac{4}{e}$
• D. $\frac{16}{e}$

Answer 1

Answer: (C)

$\frac{4}{e}$

Answer 2

y = $\left[ \left( \frac { \mathrm { n } + 1 } { \mathrm { n } } \right) \left( \frac { \mathrm { n } + 2 } { \mathrm { n } } \right) \ldots \ldots . \left( \frac { 2 \mathrm { n } } { \mathrm { n } } \right) \right] ^ { 1 / n }$

log y =

=

log y = $\int _ { 0 } ^ { 1 } \ell n$ (1 + x)dx