- #1

WMDhamnekar

MHB

- 376

- 28

- TL;DR Summary
- Proofs of ##1) \displaystyle\sum_{n=0}^\infty\frac{nX^n}{n!}= Xe^X, 2) \displaystyle\sum_{n=0}^\infty \frac{n^2X^n}{n!}= Xe^X + X^2e^X##

I know the Taylor expansion of exponential, ##\exp(x)=\displaystyle\sum_{n=0}^\infty \frac{X^n}{n!}##

But if I calculate first and second derivatives of both sides of the above formula, L.H.S and R.H.S remain the same as before i-e ##e^X##

So, how can I get the proofs of both series?

But if I calculate first and second derivatives of both sides of the above formula, L.H.S and R.H.S remain the same as before i-e ##e^X##

So, how can I get the proofs of both series?

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