(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If Sn =1/0! + 1/1! + 1/2! +.... 1/n! , Tn=(1+(1/n))^n, then lim sup Tn ≤ e? (e=2.71...)

2. Relevant equations

1. e= Ʃ(1/n!)

2. If Sn≤Tn for n≥N, then lim sup Sn ≤ lim sup Tn

3. The attempt at a solution

By binomial theorem,

Tn= 1 + 1 + 1/(2!)(1-1/n) + 1/(3!)(1-1/n)(1-2/n) + ..... + 1/n!

Hence Tn ≤ Sn＜ e,

lim sup Tn ≤ lim sup Sn＜ e

∴ lim sup Tn＜ e

But I do not get lim sup Tn ≤ e

What did i do wrong?

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# Very simple question about limit superior (or upper limit)

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