1+x22!+x44!+……∞2-x+x33!+x55!+……∞2=

1+x22+x44+……∞2-x+x33+x55+……∞2 =e+e-12-e-e-12 =144e e-1=1

1+x22!+x44!+……∞2-x+x33!+x55!+……∞2=

1+x22+x44+……∞2-x+x33+x55+……∞2 =e+e-12-e-e-12 =144e e-1=1

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${(1 + \frac{x^{2}}{2!} + \frac{x^{4}}{4!} + \dots \dots \infty)}^{2} - {(x + \frac{x^{3}}{3!} + \frac{x^{5}}{5!} + \dots \dots \infty)}^{2} =$

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Detailed Solution

$\begin{array}{rcl} {(1 + \frac{x^{2}}{2} + \frac{x^{4}}{4} + \dots \dots \infty)}^{2} - {(x + \frac{x^{3}}{3} + \frac{x^{5}}{5} + \dots \dots \infty)}^{2} \\ = & (\frac{e + e^{- 1}}{2}) - (\frac{e - e^{- 1}}{2}) \\ = & \frac{1}{4} [4 e e^{- 1}] = 1 \end{array}$