2
votes
1answer
39 views

Exponential function as a sum

I have an exercise that asks me to write $e^{2x}$ using a power series of $x+1$. I know that $$e^{2x}=\sum_{n=0}^{\infty}\frac{(2x)^{n}}{n!}$$ Then, I tried something like this $$x=y+1\Rightarrow ...
2
votes
0answers
77 views

Upper Bound on $\frac{1}{1-\beta u}-\sum\limits_{n=0}^{\infty}\frac{e^{-u}u^n}{n!(1-\beta(n+1))}$

Is there any procedure to find an upper bound of the following expression? $$\frac{1}{1-\beta u}-\sum_{n=0}^{\infty}\frac{e^{-u}u^n}{n!(1-\beta(n+1))}$$ Here $u,\beta\in\mathbb{R},\ u>1,\ ...
0
votes
1answer
94 views

Finding a general coefficient in the multiplication of the two series

Help me please to find a general coefficient $a_j$ of the following series $$ ...