# summation

1. ### Central Limit Theorem for weighted summation of random variables?

Here is a quick question:- If X1, X2, X3,.... X20 are 20 random variables (independent/ idd) What would be the result of: 2*X1+5*X2+1*X3+18*X4...+0.5*X20? (linear combination of the random variables, with fixed known constants). Will the above function form a normal distribution if we...
2. ### What is the total summation of moments at A ?

What is the total summation of moments at A? I tried \sum M_{A} = F.(d+d )-F(d+d )-F.d I am getting negative answer.
3. ### 1, 2, 3... sum/product summation

1/1+(1+2)/(1*2)+(1+2+3)/(1*2*3)+(1+2+3+4)/(1*2*3*4)...=?
4. ### Book about Summation and Product of Sequences

Hello, I would like to know if there is any book devoted to summations and product of sequences (pi notation). With theory and good exercises.
5. ### How Can I Represent These Progressions in Sigma Notation?

I would like to represent the following finite progressions in sigma notation: 1. Finding the $n^\text{th}$ term of a geometric progression: $a_n=a_1(r^{n-1})$, where $a_1$ is the first time and $r$ is the common ratio 2. The sum of a geometric progression: $S_n=a_1\frac{1-r^n}{1-r}$ 3...
6. ### Summation of series

Hi, this is my first post on here. I haven't got a clue how to solve this question. I'm familiar with AP, GP, HP, AGP, some special series... I tried, but couldn't figure out how to approach this question. I have attached two pictures, one is the question and the other one is the answer to the...
7. ### Summation Problem

Hello Guys! Can someone help me with this! How many pair of positive integers of $(m,n)$ are there satisfying $\sum_{i=1}^{n} i! = m!$ I guess it has only one pair of solution : $(m,n) =(1,1)$ Then starting and ending value of Summation should be equal as I start at $i=1$ and we need...
8. ### Summation of powers of powers

I have recently been asked to create a formula for the summation between 1 and N for 2^A^X where A is a given number and X is the variable. After attempting to approach this via various methods, I found that it end up simplifying to 2^A (1 + 2^A (1 + 2^AxA (1 + 2^AxAxA ... which suggests that...
9. ### These summations are equal?

Hello, These summation is the same? Thanks
10. ### Struggling with what I think is a summation problem.

A child places n cubic building blocks in a row to form the base of a triangular design (see figure). Each successive row contains two fewer blocks than the preceding row. Find a formula for the number of blocks N used in the design. (Hint: The number of building blocks in the design depends on...
11. ### How to write this with summation sign? (If possible)

So I just want to know if you can write this in word with a summation sign. I'm unsure how to write it correct. The numbers behind the T's are supposed to be indexes (T are not multiplied by the number behind it). (T1 + T2 + T3 + T4 + T5)/5
12. ### Sum over random vector values

I have the following expression: $\sum_{\mathbf{x}}e^{\mathbf{x}}$, where $\mathbf{x}$ is a random vector (i.e., $\mathbf{x} \in \mathbb{R}^D$ ), and $\sum_{\mathbf{x}}$ represents a sum over all possible values that $\mathbf{x}$ can assume. Now, I'm trying to rewrite this expression...

Hey there, I am really stuck with this exercise, I don't know how to proceed and get the first steps going. I understand, that I need to do some work on the index but I really don't understand how to really go for it, since m could be anything below n. Cheers
14. ### Two general sequence summation

As shown in Chinese wikipedia "Summation" For \sum_{k=1}^n p(k) \sum_{k=1}^n p(k)= \begin{pmatrix}C_n^1 & C_n^2 & \cdots & C_n^{m+1}\end{pmatrix} \begin{pmatrix} C_0^0 & 0 & \cdots & 0\\ -C_1^0 & C_1^1 & \cdots & 0\\ \vdots & \vdots & \ddots & \vdots\\ (-1)^mC_m^0 & (-1)^{m-1}C_m^1...
15. ### The Expected value of any function of X, and correct use of the summation.

Hi, I have the following exercise but, the result is different from the one given by my book. Please, can you help me to find where is the error? The discrete random variable X has probability distribution function given by: P(X = x) = \frac{1}{6} for x = 1, ..., 6. a) Find E(X^2) b)...
16. ### Sequence Summation into closed form (understanding)

Heyo. I'm in a discrete structures class right now (discrete mathematics) and this seemed like the subforum to place this question... It's less of a "figure it out for me" type of question... But I found myself disagreeing with a colleague that we usually work on homework together... But this...
17. ### How can I evaluate this summation?

This series has positive and negative terms and I am not sure how to find the summation. Thanks
18. ### A simple problem?

Hi guys, I'm trying to do some probability for AFL tipping. I've made the following equation, and I'm curious whether anyone knows how to summarize my problem any better? I've played around using a second Summation sign, but can't seem to get it right. I'm also not sure how to make p0, p-1...
19. ### Summation by method of Differences

Problem If f(r) = \frac{1}{r(r+1)} simplify f(r+1)-f(r) Hence Sum the Series \frac{1}{2(3)(4)} + \frac{1}{3(4)(5)} + \frac{1}{4(5)(6)} +.....+ \frac{1}{n(n+1)(n+2)} Now for the first part, my simplification is correct: Which is = \frac{-2}{r(r+1)(r+2)} And for the sum of the series...
20. ### Looking for an specific summation property

Hello folks, I'm looking for a summation property like below: If the property has more summations involved then better. The key point is that the sum of pi values over the summation iteration be equal to 1. Thanks in advance! :rolleyes: