How to determine \lim_{n\rightarrow\infty}n\ln(1+\frac1n)

Jaidyn Cook

Jaidyn Cook

Answered question

2022-04-26

How to determine limnnln(1+1n)

Answer & Explanation

Luke Kane

Luke Kane

Beginner2022-04-27Added 14 answers

Notice that by the continuity of ln you have
limnwnln(1+1n)=limnln((1+1n)n)=ln(limn(1+1n)n)=ln(e)=1.

Barbara Navarro

Barbara Navarro

Beginner2022-04-28Added 18 answers

For f(x)=ln(1+x),f(0)=1. Now,
f'(0)=limx0f(x)f(0)x0=limx0ln(1+x)0x0=limx0ln(1+x)x

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