# sum

1. ### Induction Proof of Sum of n positive numbers

I am not sure if this is the right place, but it does appear in my calculus book. " Proove by induction that for all n real, positive numbers a1, a2, a3, ..., an that follow the rule a1a2a3...an = 1, the following expession is true: \sum_{i=1}^{n} a_{i} \geq n " I have tried working it out...
2. ### Riemann Sum for 1/x

How to find the integral 1/x from 1 to 2 using riemann sum? ∫ 1/x dx = lim as n goes infinity Σ(i = 1 to n)f(xi)Δx Δx = 2-1/n = 1/n xi = 1 + iΔx = 1 + (i/n) = lim as n goes infinity Σ(i = 1 to n)f(1 + (i/n))(1/n) = lim as n goes infinity Σ(i = 1 to n)[ 1 / (1 + (i/n)) ] (1/n) = lim as n goes...
3. ### What is the sum of A and B?

The 4-digit number A 55 B is divisible by 36. What is the sum of A & B?
4. ### vector product and vector sum

what is the vector sum of (2,10,-50) and (30,-4,0) and also explain the definition of vector sum and vector product.vector
5. ### Riemann Sum Help

So I'm stuck on a question. I know how to do Riemann sums but I get stuck at the sub-intervals = n part. Can someone help me? f(x) = (x^3 + 1) [a,b] = [0,2] So the first question is: Find the upper Riemann sum for the definite integral with N equally spaced subintervals, expressing it in...
6. ### conditional expectation given sum

Hello, I need your help. Suppose: X\sim N(0,\sigma^2_x), Y\sim N(0,\sigma^2_y) , X, Y are independent, and c\in R. I need to find an expression (as closed form as possible) for: E[X|X+Y>c] . Thanks! Dan
7. ### Determining value of constant to give infinite sum of 2

Determine the value of constant c such that \sum _{ n=2 }^{ \infty }{ { (1+c) }^{ -n } } = 2 Apologies if i'm missing something really obvious but should this be solved simply by observing that the denominator of each term becomes infinitely smaller and thus solving the polynomial?
8. ### Find Sum of Series...Calculus 2

I am trying to find the sum of the series S_n. The question has a sigma notation from n = 1 to positive infinity. The function given is 6/[n(n + 3)]. I found the partial fraction to be (2/n) - 2/(n + 3). If this is a telescoping series, I am having trouble finding S_n. I...
9. ### Probability density function of sum 3 dependent random variables?

Suppose we have s = x+y+z and x,y and z are dependent random variables. Can I use this approach to find probability density function of S? first find CDF of S: $F_{S}(s)=P(S<=s)=\int_{-\infty}^{+\infty}dx \int_{-\infty}^{s-x}dy \int_{-\infty}^{s-x-y}f_{X,Y,Z}(x,y,z)dz$ and then differentiate it...
10. ### Finite sum question with motivation from the power series of e^x (not for the weak :)

Sorry if the image is not very clear (please tell me if it is illegible). Part a) and b) are quite straight forward. Part c)i) I did using part b) from the fact that any real number to the power of an even integer is positive. Part ii) was a little bit harder. My working out is shown below...
11. ### The sum of this infinite series?

I've tried to find the sum of this infinite series infinity sum = 1/(k(k+3)) k=1 I tried to treat it as a telescoping series.I decomposed the fractions and I've found a pattern where the negative part of a_2 cancels with the positive part of a_6.I then figured that...
12. ### Sum and difference identities help?

The following relationship is known to be true for two angles A and B: cos(A)cos(B)-sin(A)sin(B)=0.957269 Express A in terms of the angle B. Work in degrees and report numeric values accurate to 2 decimal places. Enter your answer as an expression. Be sure your variables match those in the...
13. ### Trig Product and Sum Help

Hi I am struggling with the following question. The instantaneous power, p, in an electric circuit is given by p = iv,where v is the voltage and i is the current. Calculate the maximum value of power in the circuit if v = 0.02\sin (100\pi t) volts i = 0.6\sin (100\pi t + \frac{\pi}{4} )...
14. ### Prove using Product to sum identities

Prove Cos (α – β) = cos α cos β + sin α sin β Hint:Keep the left side as is and use the Product to Sum Identities. Then, distribution to simplify the right side. I could really use some help on this..
15. ### Sum k=1...infinity (k^90*e^-k) converges or diverges?

Hi, all. I got this one incorrect and I'm wondering how to get it started. Any thoughts on a good first step? Thanks! Converges or diverges? Sum k=1...infinity (k^90*e^-k)
16. ### Does sum in the Digamma function exist?

I am reading about the Digamma function. It deduced in, that $$\psi(z)=-\gamma-\frac{1}{z}+\sum_{k=1}^{\infty}\left [ \frac{1}{k}-\frac{1}{z+k} \right ]=-\gamma+\sum_{k=0}^{\infty}\left [ \frac{z+1}{(k+1)(z+k)} \right ]$$ for all $z\in \mathbb{C}\setminus \{0,-1,-2,\cdots \}$, using the...
17. ### Express Z = ~(A * (B + C * (~A + ~B))) as a sum of products

So here's the problem that was given as well as the lecture's working out... http://i.imgur.com/5jw3Vv7.png It all makes perfect sense until the second last line, I don't understand how it goes from ~A+~B*(~C+A*B) to ~A+~B*~C+~B*A*B (Fyi for those of you who aren't familiar with this notation...
18. ### Expression for sum of numbers

1: 3,5: 7,9,11 ....sum of these groups can be expressed as n raised to 3. How can I prove this?
19. ### Number Theory-- Sum of Cubes

Let k be a prime integer such that 100 < k < 225. How many distinct values of k exist such that k = a^{3} + b^{3} where a and b are both positive integers? The answer key says 0 and I suspect this has something to do with k being prime. What's the explanation behind this?
20. ### Triangle Sum 180 from Euclid's 5th axiom

I am working on a proof of the Triangle Sum Theorem by using Euclid's 5th axiom. Attached the picture so that you can see. So I started going in the other direction and saying well if \alpha+\gamma+\beta\prime \ge 180 then also \beta+\gamma+\alpha\prime \ge 180 and started working out that...