Find the sum up to n terms: 1.1!+2.2!+3.3!+........+n.n!
Asked by | 11th Aug, 2012, 09:30: PM
Expert Answer:
We have:
a*a! = (a+1 - 1)*a! = (a+1)a! - a! = (a+1)! - a!
Hence, 1*1! + 2*2! + .... +n*n! = (2!-1!) + (3! - 2!) + .....(n + 1)! - n!.
= -1! + (n+1)! or (n+1)! - 1
Hence, 1*1! + 2*2! + .... +n*n! = (2!-1!) + (3! - 2!) + .....(n + 1)! - n!.
= -1! + (n+1)! or (n+1)! - 1
Answered by | 11th Aug, 2012, 09:39: PM
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