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Question

Find the sum of the following series:
x33!+x55!+x77!+.......

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Solution

ex=1+x1!+x22!+x33!+x44!+x55!+x66!+x77!+.... --- ( 1 )

ex=1x1!+x22!x33!+x44!x55!+x66!x77!+.... --- ( 2 )

Subtracting ( 2 ) from ( 1 ) we get,
exex=[1+x1!+x22!+x33!+x44!+x55!+x66!+x77!+..][1x1!+x22!x33!+x44!x55!+x66!x77!+..]

exex=2x+2x33!+2x55!+2x77!+..

exex2=x+x33!+x55!+x77!+..

exex2x=x33!+x55!+x77!+..


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