- #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?