SOLUTION: Find the sum of the infinite series (1 + 2 + 3 + 4 + .... + r-1) divided by r! where r is from {{{ 2 to inf }}}? [Note: Here r! means factorial of r]

Algebra ->  Sequences-and-series -> SOLUTION: Find the sum of the infinite series (1 + 2 + 3 + 4 + .... + r-1) divided by r! where r is from {{{ 2 to inf }}}? [Note: Here r! means factorial of r]      Log On


   



Question 1184396: Find the sum of the infinite series (1 + 2 + 3 + 4 + .... + r-1) divided by r! where r is from +2+to+inf+?
[Note: Here r! means factorial of r]

Answer by ikleyn(52900) About Me  (Show Source):
You can put this solution on YOUR website!
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Find the sum of the infinite series (1 + 2 + 3 + 4 + .... + r-1) divided by r! where r is from
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The sum   1 + 2 + 3 + . . . + (r-1)  is  %28r%2A%28r-1%29%29%2F2.


This sum divided by  r! is  %281%2F2%29%2A%281%2F%28r-2%29%21%29.


So, the problem asks about this sum  %281%2F2%29%2Asum%281%2F%28r-2%29%21%2C2%2Cinfinity%29.


It is the same as the expression  %281%2F2%29%2Asum%281%2Fr%21%2C0%2Cinfinity%29.


The last expression value is  e%2F2,  where  "e"  is the base of natural logarithms.


ANSWER.  The requested sum is equal to  e%2F2 = 2.71828%2F2 = 1.35914  (rounded).

Solved, answered and explained.