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Simplify 2 / 1! + 2 / 3! +... + n / (n + 1)! 1/2!+2/3!+...+n/(n+1)!
The first one is 1 / 2!
n/(n+1)!
=[(n+1)-1]/(n+1)!
=(n+1)/(n+1)!-1/(n+1)!
=1/n!-1/(n+1)!
So = 1 / 1! - 1 / 2! + +1/n!-1/(n+1)!
=1-1/(n+1)!
How to simplify this? 3 ^ n - 3 ^ (n-1)
Original formula = 3 ^ n - (3 ^ n)
N times of 3 minus n-1 times of 3
3^N-3^(N-1)
=3^(N-1) *(3-1)
=2*3^(N-1)
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