# sum

1. ### Sum of rational cubes: I would like to know if this formula was already discovered (some book, references ..please...)

Hello People The problem finding sum of two rational cubes to give an integer is not an easy one: it has the general form a^3 + b^3 = n . c^3 example find (a/c)^3 + (b/c)^3 = 7 (or a^3 + b^3 = 7 . c^3 ) The are infinite solutions for this one, the first being (5/3)^3 + (4/3)^3 = 7 , (...
2. ### absolutely convergent series

Hello. I want to show that, for an absolutely convergent series \sum_{n=1}^{\infty}a_n, we have \left|\sum_{n=1}^{\infty}a_n\right|\leq\sum_{n=1}^{\infty}|a_n|. Let M be an positive integer. I begin with the triangle inequality \left|\sum_{n=1}^{M}a_n\right|\leq\sum_{n=1}^{M}|a_n| and taking...
3. ### Compute infinite sum

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

Hello all, Calculate \sum_{k=n}^{k=1} k. All the best, Integrator
5. ### Having Sum Fun Counting Ordinals

This is a draft. Knowing me, it is probably nonsensical and filled with errors. I'm trying to enumerate some very large countable ordinal assuming of course that math isn't broken and I can't enumerate $\omega_1$ itself. ... And no, jic, I don't think math is broken. Why? Do you? :spin...
6. ### Is there a way to obtain the modulus of desired sum from these vectors?

The problem is as follows: Find the modulus of the resultant vector which are seen in the quadrilateral shown below. Consider M and N to be mid points and \overline{MN}=20 The alternatives given on my book are: $\begin{array}{ll} 1.&20\\ 2.&40\\ 3.&60\\ 4.&80\\ 5.&50\\ \end{array}$ I'm...
7. ### How can I find the sum of vectors in this triangle?

The problem is as follows: Using the figure from below find the modulus of the resultant vector if it is known $\left\|v\right\|=3$ and $\left\|u\right\|=5$. The alternatives given on my book are: $\begin{array}{ll} 1.&7\\ 2.&10\\ 3.&14\\ 4.&23\\ 5.&28\\ \end{array}$ I...
8. ### Inequality similiar to harmonic sum

For which values of n the inequality holds true : 1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{n^4 }=\sum_{j=1}^{n^4 }j^{-1} >2n.
9. ### Express any number greater than 35 as sum of x 5s and y 9s

How can we prove that any number greater than or equal to 35 as a sum of x 5s and y 9s Probably by induction
10. ### How to simplify a sum of multiples of secants?

I've got tangled into this problem, so I hope somebody could help me. The problem is as follows: Find the value of $\textrm{H}$ which belongs to a certain vibration coming from a magnet. $$H=\sec \frac{2\pi}{7}+\sec \frac{4\pi}{7}+\sec \frac{6\pi}{7}$$ It was easy to spot that each term was...
11. ### Sum of number's number

Hey, I have a number theory problem: determine the sum of the digits of a natural number. I have been thinking about it for a lot time during this days, but I can't still find a solution. Can someone give me an idea or advise me a book/internet site with something useful? Thank a lot.
12. ### Sum of the digits

Please help my to solve this problem: $N = 1111 â€¦.11$ (a total of 1989 digits). What will be the sum of the digits of $N^2$? My attempt was like: sum of the digits of $N^2=($sum of the digits of $N)^2$ But I was wrong because this will only work for up to 9 digits. I really appreciate your...
13. ### Probability of Sum of Balls Drawn

Hi, I'm sure this is simpler than my brain is making it out to be but I need help... So, we've got a bag of 20 balls and the user draws 3 balls out. I'm trying to work out the probability of the total value of those 3 balls being 4-5 or 6 and over. The balls have the following values and...
14. ### Infinite sum

Show whether the series diverge or converge : \sum_{n=1}^{\infty} \sqrt[n!]{\sin^{n} (n^{2}\cdot 2^{n})}.
15. ### the sum

Find the sum of 1+11+111+1111+ .....1.....1 to the n th term in term of n.
16. ### Series sum

The sum of series $$\frac{5}{2!\cdot 3}+\frac{5\cdot 7}{3!\cdot 3^3}+\frac{5\cdot 7\cdot 9}{4!\cdot 3^3}+\cdots \cdots \infty$$
17. ### Series sum proof

How to prove it or disprove it? Is it true? \sum_{j=1}^{\infty} \lfloor \frac{n}{2^j }\rfloor=n+1 \; , n,j \in \mathbb{N}.
18. ### Series Sum

Evaluation of $$\sum^{\infty}_{k=1}\frac{1}{k\cdot 2^k}$$
19. ### Vanishing Sum of Roots of unity

Hi everyone, I am new here. I have been trying to figure out how to attack multiple problems involving cyclotomic polynomials, roots of unity, number fields, and other number theory subjects related to those. One particular problem I am stuck on is the following: Let $n$ and $p$ be primes...
20. ### Linear algebra, sum of subspaces

Let U1, U2, U3 be subspaces of R^4: U1 = {(a,b,c,d):a=b=c} U2 = {(a,b,c,d):a+b-c+d=0; c-2d=0} U3={(a,b,c,d):3a+d=0} show that: a) U1 + U2 = R^4; b) U2 + U3 = R^4; c) U1 + U3 = R^4; whish of the sums are direct sum?