Tagged Questions

For questions about recurrence relations, convergence tests, and identifying sequences. For questions on finite sums use the (summation) instead.

2answers
91 views

How find all possible values of $a_{2015}$ for $a_2 = 5$, $a_{2014} = 2015$, and $a_n=a_{a_{n-1}}$?

Let $(a_i)_{i\in \Bbb{N}}$ be a sequence of nonnegative integers such that $a_2 = 5$, $a_{2014} = 2015$, and $a_n=a_{a_{n-1}}$ for all other positive $n$. How find all possible values of $a_{2015}$?
1answer
226 views

How to work out following problem -> “sum of the multiples of 6 less than 100”

I'm not sure how to approach this without just brute forcing it, which would be doable for numbers lower than 100 but obviously not great and certainly not for 2000 or something. I know that the ...
1answer
193 views

1answer
62 views

Series convergence or divergence how to test

I have the following series defined. $$\displaystyle\sum_{k=1}^{n} \cos \left( {\frac{\pi}{2}} k \right) \frac{k}{k+1000} \frac{1}{\sqrt{k}}$$ where $n = 1,2...$ How to test whether this series ...
2answers
65 views

1answer
31 views

0answers
23 views

Approximating ArcCos(x) without Radicals

Take $$f(x)=2x\arccos\left(\frac{x^2+d^2-1}{2xd}\right)$$ and try and find $$I(x)=\int_{d-1}^{3}dx f(x) \sqrt{\left(\frac{x-1}{x}\right)}\left(3-x\right)^3$$ You'll find the result is messy (see ...
1answer
431 views

Determine the region of convergence of series of complex functions

I have this problem. Find the region of convergence of the following series of complex functions $$\sum_{n=1}^\infty \frac{2^n}{z^{2n}+1}$$ The progress I have made so far is that when n goes to ...
2answers
126 views

Help me understand how to take derivative of the PDF of X~binom(n,p) with respect to p.

This is the solution I was given. My questions: Why is it summed from k=1 to x. Shouldn't it be from k=1 to n? (If not, why not?) What is happening to the first term from line 1 to line 2? When we ...
1answer
145 views

Is there a systematic way of resolving sequences of dots in figures?

http://bibliotecadigital.ilce.edu.mx/sites/telesecundaria/tsm01g01v01/u02t04s01.html I wonder if there is a systematic way to get the formula of a sequence of dots in figures, to resolve it faster, ...