# infinite

1. ### Compute infinite sum

Compute: \sum_{k=1}^{\infty } \frac{\sin(kn\pi )}{k}\; , n\in \mathbb{N}.
2. ### Compute infinite product

Compute \prod_{n=1}^{\infty} (1-\frac{2}{n^2 }).
3. ### Infinite Continued Fractions

I need help with ICFs, specifically calculating sum with algebra and/or simple calculus. $$A=a_1 + \cfrac{1}{a_2 + \cfrac{1}{a_3 + \cfrac{1}{a_4 + ....}}},$$ where $a_n = f(n), \; n \in \mathbb{Z}^+$. (?) Is the fraction above always convergent if $a_n \ge 1$? (?) What about \$ 0 < a_n <...
4. ### Infinite series

hi I found this infinite series in my calculations and I want to ask if it's have a name . I attached it to this thread. if anyone here knows anything about it ,please contact me.
5. ### Median between infinite sets

Is the "midpoint" between the sets of numbers approaching positive infinity and negative infinity definable as the set of countable numbers?
6. ### Infinite primes

Prove that there are infinite prime numbers of form : p=1+n! .
7. ### Infinite series

I cannot remember the infinite series for \sqrt {1 - a} for 0 < a <<1
8. ### Infinite sum

Show whether the series diverge or converge : \sum_{n=1}^{\infty} \sqrt[n!]{\sin^{n} (n^{2}\cdot 2^{n})}.
9. ### Can an infinite sequence be missing one of such sequences?

Can an infinite sequence of finite sequences of combinations of a finite number of elements be missing one of such finite sequences? (If the rules do not prohibit such a finite sequence.)
10. ### Ðn infinite number of experiments testing a process

For an infinite number of experiments testing a process â€” a process that can be represented as an arbitrarily long finite sequence of combinations of a finite set of elements â€” should each such process occur?
11. ### An infinite set of finite sequences of combinations of a finite set of elements

An infinite set of finite sequences of combinations of a finite set of elements is an infinite uncountable set?
12. ### The number of all combinations of limited number of elements is infinite?

The number of all possible consecutive combinations (sequences with beginning and end, finite sequences) of a limited number of elements with a limited number of changes from one combination to another (in one sequence) is infinite?
13. ### Infinite product

How to show whether the infinite product converges ? p=\prod_{n=1}^{\infty } \prod_{m=1}^{\infty } \frac{n}{10^{m}} \; \; , n,m \in \mathbb{N} . Is p the product of all numbers in interval (0,1) ?
14. ### Infinitesimal and Infinite and Foundations of Calculus

INFINITESIMAL: Arbitrarily small distance between two points which can never equal zero. Basis of derivative. Example: Divide a line into n seqments. As n becomes infinite the distance between points becomes infinitesimal. Basis of integral. n never equals infinity, you can never get there...
15. ### Infinite primes question

Are there infinitely many primes of form p=1+n! \;
16. ### Infinite solutions problem

I am trying to solve following problem. I am trying to find x,y,z in terms of \lambda. And then equating the resultant equation to 0. Am I correct?
17. ### infinite series

Find 3/13+33/13^2+333/13^3+3333/13^4+....
18. ### Infinite Sums

T = 1/2 + 1/4 + 2/8 + 3/16 + 5/32 + 8/64 The numerator of each subsequent term is the sum of the numerators of the previous two terms. The denominator of each subsequent term is twice the denominator of the previous term. 1) By considering the first six terms of 1/2 T and 1/4 T, find the...
19. ### Infinite convergent series.

How do I find the limiting value of any convergent series ? I mean, how do I approach it? ("steps", maybe?) ex : (1^-2)+(2^-2)+(3^-2)+.... = pi^2/6 I know the solution of this problem but how on earth did anyone (Euler) come up with this ? . . . . . ( I'm trying to solve this...
20. ### Cantor's Infinite Binary Sequence

Let Ln be the list of n-place binary sequences: 00......00 n-binary digits 00......01 00......10 00......11 00....100 ............ 1111111 n-ones What is the difference between \lim_{n \rightarrow \infty}Ln and Cantor's list* of infinite binary sequences? *...