All Questions
1,809
questions
4
votes
2
answers
275
views
Can someone please explain to me how I did this summation formula wrong?
I was trying to show that
$\sum \limits_{k=1}^n k^2 = \frac{n(n+1)(2n+1)}{6}$ but instead I got this $[\frac{n(n+1)}{2}]^2$ which from my understanding I basically proved another summation formula ...
- 2,780
2
votes
2
answers
12k
views
how to determine variable n when not given in Simpson's Rule problem
I have $$\int_0^2 \frac{1}{1+x^6} dx$$
We vaguely went over this in class today and I understand how to work Simpson's rule but only when I have $n$ already given to me. How can I determine $n$ when ...
- 211k
2
votes
1
answer
42
views
Where am I making my mistake? (intervals of convergence)
The sum is:
\begin{align}
\sum_{n=1}^{\infty} \frac{(x-6)^n}{(-8)^nn}
\end{align}
I end up with $|(x - 6)/8| < 1$ and therefore, $-8 < 6 - x < 8$ so $14 > x > -2$, but that gives me the ...
- 25.7k
1
vote
1
answer
177
views
Riemann Sum Integration problem
I do not understand how to start this problem. I know I have to integrate from 0 to 1 and that n=3 but thats all. Hints/clues appreciated!
- 213k
3
votes
1
answer
3k
views
Partial derivative of a summation.
I am trying to confirm a stated result on my lecture slide.
Question:
Given that $A:= \sum_i^n \frac{a_i}{(1+b)^{t_i}}$, where $a_i,b \in \mathbb{R}_+$ and $t_i \in \{t_1,...,t_n\}$ where $0 < ...
- 30k
1
vote
4
answers
433
views
Find $\sum_{n=1}^{\infty}\frac{1}{n!}$
Find $$\sum_{n=1}^{\infty}\frac{1}{n!}$$
All of the advice I've seen to compute this sum says to use the ratio test, but this is in a chapter BEFORE the ratio test, so the book wants me to solve this ...
3
votes
2
answers
143
views
Infinite Geometric Sum
So I have this infinite sum:
$$\sum_{k=-\infty}^\infty \left(\frac{1}{2}\right)^{|k|}=3 \tag{1}$$
Which breaks down to:
$$\sum_{k=-\infty}^{-1}2^{k} + \sum_{k=0}^\infty \left(\frac{1}{2}\right)^{k} \...
- 104k
1
vote
2
answers
303
views
Question about summation notation index
I'm working through a proof involving the sum of covariances but the notation is tripping me up. What does it mean when you are taking a summation over the index $i < j$? For instance $\sum_{i &...
CommunityBot
- 1
0
votes
1
answer
59
views
Complex analysis equality in a limited sum
Let $z=e^{i\theta}$ with $\theta \in [0,2\pi[$ . Consider the sum
$$
\sum_{n=1}^{N} (e^{i\theta})^n.
$$
How could this be equal to
$$
\frac{1-e^{iN+T\theta}}{1-e^{i\theta}} \quad ?
$$
I tried to ...
CommunityBot
- 1