Question

2!/1! +3!/2!+...... +(n+1)!/n! = n*(n+3)/2
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Answer 1

2!/1! + 3!/2! + ... +(n+1)!/n! = 2+3+...+(n+1) = 1 + 2 + 3 + ... + (n+1) - 1 =    
= (n+1)(n+2)/2 - 1 = (n² + 3n + 2 - 2)/2 = (n² + 3n)/2 = n(n+3)/2