Recent content by wanchosen

Thanks!

I have been stuck on this question for a while and have not got much success from class mates...can somebody please help? Using an appropriate convergence test, find the values of x \in R for which the following series is convergent: \sumn=1n \frac{1}{e^n * n^x} So, Un = \frac{1}{e^n...

Yes, I had misunderstood the ()n. I believe, effectively the series is :- \sumn \frac{1}{e^n * n^x} If Un = \frac{1}{e^n * n^x} and U(n+1) = \frac{1}{e^(n+1) * (n+1)^x} then U(n+1)/Un = \frac{n^x}{e * (n+1)^x} Therefore if the series is convergent: \frac{n^x}{(n+1)^x} < e...

I assumed because the whole expression is encased in ()n that we summed all terms for each value of k upto n.

I am having problems with the following question: Using an appropriate convergence test, find the values of x \in R for which the following series is convergent: (\sumnk=1 1/ekkx)n I used the ratio test to solve this but I'm not so sure about my solution: n1 = \frac{1}{e} n2 =...

Thanks Pere

I have been looking at the following problem but have doubts about my solution: Suppose you are told that a particular team has won w games, drawn d games and lost l games during the course of a season. Calculate the probability that a) the team won both the first and last games of the...

Thanks HallsofIvy, Your method makes sense. Just to clarify:- "To solve (2x+ 3)/(x- 5)< |(4x+12)/(x+1)|, look at (2x+3)/(x-5)= |(4x+5)/(x+1)|." Did you mean "look at (2x+3)/(x-5)= |(4x+12)/(x+1)|"? I found the first two roots by equating the equations and multiplying both sides by...

I have been trying to solve the following inequality. Solve the equation: (2x+3)/(x-5)<¦(4x+12)/(x+1)¦ (where ¦¦ is meant to be modulus) I tried to solve this, firstly by using the positive modulus: (2x+3)/(x-5)<(4x+12)/(x+1) which gives me two solutions:- 1) x< (13-SQRT(673))/4 and 2)...

Thanks, tried completing the square to solve the quadratic and this worked.

Completing the square, or using the quadratic formula are another two methods.

I assumed that I need to get all the trig functions of the same type before I can solve for x. Using the identity for sec^2(x) seemed the obvious choice...which lead me to a quadratic. I couldn't see how else to solve for x. I also tried converting everything in terms of cos (x) which was more...

Hi there, I am struggling to solve for x in the following problem:- Find all values of x in the interval 0<= x <= 360 for which: tan^2(x) = 5sec(x) - 2 I have used the identity tan^2(x) + 1 = sec^2(x) to get: sec^2(x) - 1 = 5sec(x) - 2 and rearranged to get sec^2(x) - 5sec(x) +...

Hi tiny-tim, Thank you so much for that. That makes sense now! It was much easier working with the relative velocity! I completely forgot about adding the original time T to travel to the first collision! Thanks again.

Hi there, I have been struggling with this problem for a while. It's an A-Level Mechanics problem. A smooth groove in the form of a circle of radius a is carved out of a horizontal table. Two small spheres, A and B, lie at rest in the groove at opposite ends of a diameter. At time t = 0...