# summing

1. ### Summing series cos (n theta) / n^2

Can anybody help with summing the series cos (n theta) / n^2 from n= 1 to infinity?
2. ### Summing puzzle

Here is a sequence : 01 10 1001 10010110 1001011001101001 ..... Let us write the same sequence without spaces 01101001100101101001011001101001 .... Starting from left to right and replacing each digit one by its rank 2 3 5 8 9 12 14 15 17 Can you find the formula to compute the sum S(n)...
3. ### partial fractions for summing series

how did it find this 1-1/(n+1) ? if is subtract 1/n - 1/n+1 the result is different
4. ### Summing Regressors in a regression

Can you sum the co-efficients on regressors to get a better approximation of something? And then get the 95% confidence interval? If so how would you do this? To me this would be a problem as you can't sum standard errors which are necessary for getting the confidence interval? So you would...
5. ### Summing a series problem

Hi There, i am trying to sum up a sequence of numbers using the summing rule for 1 + a^1 + a^2 + a^3 + a^4 +... + a^n = (a^n - 1/(a-1), for this sequence: 1/9 + 1/9^2 + 1/9^3 + .. + 1/9^n. Is it as simple as just inverting the formula ie : ((a^n - 1/(a-1))^-1 ?? What about the 1 that...
6. ### Am I summing this correctly?

I have this series (1-v^39) + (1-v^36) +(1-v^33).....+(1-v^3) I added up all the 1's and was left with: 13-(v^3 +v^6....+v^39) Factored out v^3 13- v^3(1+v^3 +..... v^36) So I get 13 - v^3 * [(1-v^37)/(1-v)]
7. ### What is the symbol for summing odd numbers?

What would I use instead of \sum if I just wanted to sum odd values for some number n through k?
8. ### Help Summing Difficult Function

Hey everyone, this is my first thread, and I hope it will give me a good experience on this site. Anyway, onto the question: I have been trying to figure out a way to sum this: \lim_{n\to\infty}\frac{r}{n}\sum_{i=0}^n\sqrt{r^2-x_i^2}\Delta x Where x_i=\frac{ri}{n} and \Delta...
9. ### Summing a complex series

Hi, here is a problem involving summing a series involving a complex equation. Sum this series: a_1 + a_2 + ... + a_{99} where a_n = \frac{1}{(n + 1)\sqrt{n} + n\sqrt{n + 1}} for n = 1, 2, ..., 99 I'm not exactly sure how to start this question. Please help, BG
10. ### Summing a geometric series

Hi all. I have been asked to sum this series: 1+4x+7x^2+10x^3+...+(3N-2)x^N and also asked what the sum is to infinity when |x|< 1 I have all of the formulae (dodgy spelling :) ) for summing a series and sum to infinity but this one has me stumped; mainly because at the back of the text book...
11. ### Summing numbers 0 to 100

Suppose you have a list of numbers from zero to one hundred. How quickly can you add them all up without using a calculator?
12. ### Summing an Infinite Series

Hello. I'm stuck on another proof. Can anyone help me with this problem? Let S of N be the Nth partial sum of the harmonic series \sum_{n=1}^{\infty}\frac{1}{n} a) Verify the following inequality for n=1,2,3. Then prove it for general n. \frac{1}{2^{n-1} + 2} + \frac{1}{2^{n-1}...
13. ### GrouPing and SuMMing

THE number 1 to 12 are to be grouped into 3 groups of 4 numbers each. The numbers in each group are summed up. How many smallest sums can there be if it is different from the other 2 sums in that grouping? *show working and explanation PLS (Nod)
14. ### Summing Series -2 questions.

Hey, I've got 2 unsolved problems that need help! 1. Find the sum of the multiples of 7 which are less than 10000. My answer is 714264285 but the book says 7142142? 2. Find the sum of the series n + 2(n-1) + 3(n-2) +...+ n. A step by step guide would be really appreciated for this one...
15. ### Summing areas of squares

A square S1 has a perimeter of 40 inches. The vertices of a second square S2 are the midpoints of the sides of S1. The vertices of a third square S3 are the midpoints the sides of S2. Assume the process continues indefinitely, with the vertices of S K+1 being the midpoints of the sides of Sk...
16. ### Summing proof

Let n be a nonnegative integer. Use the identity {(1 + x)^n}{(1 + x)^n} = {(1 + x)^{2n}} To show that \sum_{k=0}^n {n \choose k}^2 = {2n \choose n}. So far ive gotten to... Using the binomial theorem; (x + y)^n = \sum_{k=0}^n {n \choose k} x^{n-k}y^k and setting x and y to one...
17. ### Induction with summing

Now i usually can do induction problems but i cant figure out what to do when theres summing involved. Can anyone help with the following question? Prove by induction: \sum_{k=1}^n (-1)^2 k^2 = \frac{1}{2}(-1)^nn(n+1) It works for n = 1 so we have our inductive phase... Now assuming n is...
18. ### Summing - question

Hey guys, just a quick query. The question says: Find, as polynomials in n, the sum of 1.2.3 + 2.3.4 + ..... + n(n+1)(n+2) _______________________________________________________ Is that simply \Sigma_{k=1}^{n} k(k+1)(k+2) = \Sigma_{k=1}^{n} k^3 + 3 \Sigma_{k=1}^{n} k^2 + 2...
19. ### summing series

Can someone help me please Thanx Edgar Suppose a is a real number and it is not an integer. Calculate sigma between n= - infinity to n= infinity [1/(n+a)^2]
20. ### Java Program - Summing Integers

Hi guys--I have to write a program that reads a set of integers and then finds and prints the sum of the even and odd integers. For instance, if the numbers were: 9, 10, 17, -20, 22, -3 evens should be 12 odds 23 all 35 I'm messing up the math but here's what I have below--help...