- #1

jwqwerty

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## Homework Statement

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

## Homework Equations

1. e= Ʃ(1/n!)

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

## 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?