Summing a Factorial Series

Algebra Level 3

$\large 1(1!) + 2(2!) + 3(3!) + \cdots+ 7(7!) =\, ?$

Notation :
$!$ denotes the factorial notation. For example, $8! = 1\times2\times3\times\cdots\times8$ .

The answer is 40319.

1 solution

Tushar Showrav
Apr 10, 2016

We have ,
1(1!) + 2(2!) + 3(3!) + ........ + 7(7!) .
So,
Find the sum of the series,
1(1!) + 2(2!) + 3(3!) + ........ + (n-1)[(n-1) !] + n(n!)
= 2(1!) + 3(2!) + 4(3!) + ......+n[(n-1) !] + (n+1)(n!) - 1! - 2! - 3! - ....... - [(n-1)! ] - n!
= (n+1)(n!) - 1!
= [(n+1)!] - 1 .

So , we got the law . Now by puting 7 in the law we will get the answer . The answer is,
= (7+1)! - 1
= 40319 .

Nice Problem

Abhiram Rao - 5 years, 1 month ago

Summing a Factorial Series

The answer is 40319.

1 solution

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