If you know the estimation of e as (1+1/x)^x as x goes to infinity, you probably identify the expression as three special cases. x = 1, 100 and 1000. The function is monotonically increasing therefore it is quite straightforward if you know calculus.

However, it is still possible to prove it use elementary math. Here I present one for you.

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0:00 Easy Question
0:16 Solution One for Easy Question
1:20 Solution Two for Easy Question
1:38 Harder Question
1:49 Solution
3:19 Outro