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...