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Question

Show that 1+12!+14!+.......=12(e+1e).

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Solution

We have,
ex=1+x1!+x22!+x33!+x44!+........
Then e=1+11!+12!+13!+14!+............(1)
And
e1=111!+12!13!+14!............(2).
Now adding (1) and (2) we get,
(e+1e)=2(1+12!+14!+.....)
or, 12(e+1e)=(1+12!+14!+.....)

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