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lim [n 2 -n+1/n 2 -n-1] n(n-1) n_# # is infinity

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

Grade:7

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
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Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 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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