All Questions
3
questions
3
votes
2
answers
2k
views
Partial sums of $nx^n$
WolframAlpha claims:
$$\sum_{n=0}^m n x^n = \frac{(m x - m - 1) x^{m + 1} + x}{(1 - x)^2} \tag{1}$$
I know that one can differentiate the geometric series to compute $(1)$ when it is a series, i.e. $m=...
- 11.8k
1
vote
5
answers
436
views
Finit Sum $\sum\limits_{i=1}^{100}i^8-2 i^2$
Can anyone help me?
How can I find
$$\sum_{i=1}^{100}i^8-2i^2 $$
- 331
3
votes
2
answers
33k
views
Finding the infinite sum of $e^{-n}$ using integrals
I am trying to understand this:
$\displaystyle \sum_{n=1}^{\infty} e^{-n}$ using integrals, what I have though:
$= \displaystyle \lim_{m\to\infty} \sum_{n=1}^{m} e^{-n}$
$= \displaystyle \lim_{m\...
- 11.2k