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Question: \[\frac{x^{2} - y^{2}}{1!} + \frac{x^{4} - y^{4}}{2!} + \frac{x^{6} - y^{6}}{3!} + ......\infty =\]...

x2−y21!+x4−y42!+x6−y63!+......∞=\frac{x^{2} - y^{2}}{1!} + \frac{x^{4} - y^{4}}{2!} + \frac{x^{6} - y^{6}}{3!} + ......\infty =

A

ex−eye^{x} - e^{y}

B

ex2−ey2e^{x^{2}} - e^{y^{2}}

C

2+ex2−ey22 + e^{x^{2}} - e^{y^{2}}

D

ex−ey2\frac{e^{x} - e^{y}}{2}

Answer

ex2−ey2e^{x^{2}} - e^{y^{2}}

Explanation

Solution

121⋅2!+12+222⋅3!+12+22+323⋅4!+..+12+22+...+n2n⋅(n+1)!+...∞\frac{1^{2}}{1 \cdot 2!} + \frac{1^{2} + 2^{2}}{2 \cdot 3!} + \frac{1^{2} + 2^{2} + 3^{2}}{3 \cdot 4!} + .. + \frac{1^{2} + 2^{2} + ... + n^{2}}{n \cdot (n + 1)!} + ...\infty.