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Find the sum of 1x1!+2x2!+3x3!+4x4!+5x5!+..........+nxn!

Find the sum of 1x1!+2x2!+3x3!+4x4!+5x5!+..........+nxn!

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4 Answers

renu akunuri
37 Points
11 years ago

sum of the given series is " n!*n*(n+1)/2 "

take sum of factorial as value and do sumation tosum of n terms

n!*En (it is not E but the sign of sumation)

mayank varsdani
18 Points
9 years ago
actaully (n+1)!-1 is real ans
onesiforus ristya
8 Points
9 years ago
how to proff?
J3C S20266 ??? CHEOK CALVERT
26 Points
2 years ago
Let’s try when n=5,
1=2-1
2=3-1 etc.

(2-1)1! + (3-1)2! + (4-1)3! + (5-1)4! + (6-1)5!
= (2x1! – 1x1!) + (3x2! – 1x2!) + (4x3! – 1x3!) + (5x4! – 1x4!) + (6x5!-1x5!)

Notice that:
2x1! = 2!, 3x2! = 3! etc.

Thus,
=2! – 1! + 3! – 2! + 4! – 3! + 5! – 4! + 6! - 5!
 
All of them are eliminated, left with 6! -1!

Thus when n = 5, this series = (5+1)!-1

(n+1)!-1.
 

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