Dec 9, 2014 · 65 $\begingroup$ This question already has answers here: Proving the identity $\sum_ {k=1}^n {k^3} = \big (\sum_ {k=1}^n k\big)^2$ without induction (31 answers)

Jun 28, 2020 · By the ratio test, every x value between -1 and 5 would make the series converge. we just need to find out whether x=-1, 5 makes it converge. x=-1: The series will look like this. …

Question: Express the function $\frac {n^3} {1000} - 100n^2 - 100n + 3$ in terms of the Θ notation and prove that your expression in fact fits into the Θ definition ...

Mar 25, 2013 · Need guidance on this proof by mathematical induction. I am new to this type of math and don't know how exactly to get started. $$ 1^3 + 2^3 + 3^3 + \ldots + n^3 = \left [\frac …

Sep 8, 2020 · $\sum_ {m=1}^ {\infty}\sum_ {n=1}^ {\infty} \frac {m²n} {n3^m +m3^n}$. I replaced m by n,n by m and sum both which gives term $\frac {mn (m+n)} {n3^m +m3^n}$.how to do further?

Oct 29, 2017 · 112 values is the number of positive values whose n/3 and n*3 both are 4-digit numbers.

Oct 16, 2014 · Number of possible permutations of n1 1's, n2 2's, n3 3's, n4 4's such that no two adjacent elements are same? Ask Question Asked 11 years, 1 month ago Modified 7 years, 3 …

Sep 15, 2020 · where the summation is over all triples (n1,n2,n3) (n 1, n 2, n 3) of non-negative integers with sum n n. This I know how to prove: Use the definition of Multinomial Theorem to …

Feb 14, 2012 · 50 $$ \sum_ {n=1}^ {\infty} \frac { (\sin n+2)^n} {n3^n}$$ Does it converge or diverge? Can we have a rigorous proof that is not probabilistic? For reference, this question is …

Mar 12, 2020 · I was dealing with a problem on tetration and am supposed to explain why this problem was challenging to me- obviously, difficulties stemmed from the amazing growth of …