what is the difference between sum of first n primes and prime(prime(n?

Please -- if you can think of a way to reword this please do. I am wondering also if there is a simple name for this phenomenon, or if there are cases where it's not true. Example: Given an array of random numbers with an even number of elements, sorted...

Given the set [math] \{ a_1, ..., a_n \} [/math] where [math]a_i \in \mathbb{N}[/math], find two subset [math]A[/math] and [math]B[/math] such that: [math]A \cap B = \emptyset[/math] [math] card(A) = card(B) = k > 0[/math] where [math] 2k \le n...

The sum of the first 50 terms of an arithmetic sequence is 100. If the common difference (d) is increased by 3, what is the new sum?

Hi, I have used the method of differences (also called a telescoping series) to solve various maths problems before but I don't feel I understand the mechanics of it. I began looking for a more general definition of it and found this in the Mathematical...

I'm looking for formulas including (preferably convergent) sums or products over all primes, as in product [p in P] (1/(1-p^(-s))) = zeta(s) = sum [n=1 to infinity] 1/n^s [s>1] I'd like to collect here as many similar facts about the set of all primes...