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Find the sum of the series e^(x-(1)/(2)(...

Find the sum of the series `e^(x-(1)/(2)(x -1)^(2) + (1)/(3) (x -1)^(3) - (1)/(4) (x -1)^(4) + ...`

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Verified by Experts

We have,
` e^(x-(1)/(2)(x -1)^(2) + (1)/(3) (x -1)^(3) - (1)/(4) (x -1)^(4) + ...`
`=e^({(x-1)(1)/(2)(x -1)^(2) + (1)/(3) (x -1)^(3) - (1)/(4) (x -1)^(4) + ..."to"oo}+1)`
` e.e^(log_(2)(1 + x -1))`
`e.e^(log_(e) x)`= ex
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