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if I have the limit as n goes to infinity of (1+1/n)^n = e.

How do I evaluate the limit as n goes to infinity of (1+2/n)^n?

2006-11-01 16:20:42 · 2 answers · asked by ? 1 in Science & Mathematics Mathematics

2 answers

(1+2/n)^n
= [(1 + 2/n)^n/2]²

= {[1 + 1/(n/2)]^n/2}²
= [(1 + 1/p)^p]²

Note: As n→∞, n/2 →∞ ie p→∞

So lim n→∞(1+2/n)^n
= lim p→∞[(1 + 1/p)^p]²
= e²

In fact you could now argue that lim n→∞(1+p/n)^n = e^p

2006-11-01 16:38:41 · answer #1 · answered by Wal C 6 · 1 0

(1+2/n)^n=e^(1/2)

2006-11-02 00:30:42 · answer #2 · answered by JAMES 4 · 0 2

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