Complicated fraction!

Calculus Level 1

Find the value of lim ⁡ n → ∞ ( 1 + 1 n ) n ∑ k = 0 n 1 k ! \lim _{ n\rightarrow \infty }{ \frac { { \left( 1+\frac { 1 }{ n } \right) }^{ n } }{ \sum _{ k=0 }^{ n }{ \frac { 1 }{ k! } } } }


The answer is 1.

Lee Young Kyu by Lee Young Kyu , 25, Hong Kong

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1 solution

Rohit Sachdeva
Aug 29, 2014

The numerator part is a rule:

lim_{n→∞} (1+1/n)ⁿ = e

The denominator is an expansion for e

e=1+(1/1!)+(1/2!)+(1/3!)+.......∞

Hence the answer is 1

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