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Differential Calculus> lim [n 2 -n+1/n 2 -n-1] n(n-1) n_# # is i...

question mark

lim [n²-n+1/n²-n-1]^n(n-1)
n_#
# is infinity

Pushkar Aditya , 11 Years ago

Grade 7

2 Answers

Jitender Singh

Last Activity: 10 Years ago

Jitender Singh

Last Activity: 10 Years ago

Hello student,
Please find answer to your question
$L = \lim_{n\rightarrow \infty }[\frac{n^{2}-n+1}{n^{2}-n-1}]^{n(n-1)}$
$L = \lim_{n\rightarrow \infty }[1+\frac{n^{2}-n+1}{n^{2}-n-1}-1]^{n(n-1)}$
$L = \lim_{n\rightarrow \infty }[1+\frac{2}{n^{2}-n-1}]^{n(n-1)}$
$L = \lim_{n\rightarrow \infty }[1+\frac{2}{n^{2}-n-1}]^{n(n-1).\frac{2}{n^{2}-n-1}.\frac{n^{2}-n-1}{2}}$
$L = e^{\lim_{n\rightarrow \infty }\frac{2n(n-1)}{n^{2}-n-1}}$
$L = e^{2}$

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