Recent content by Ryuky

Thank you for your response. I got it now, the fraction reduces to n!/(n+1)^n = Product from 1 to n of (n/(n+1))^n which leads to n!=(n+1)^n * the Product, but then the last term of the product cancels out with (n+1)^n and so comes the required result. However, I am still interested on how you...

Hello all. I am doing a school paper on Stirling's formula and I want first to show how the factor e comes into place. So I found somewhere on the net the definition n! = (1-1/2)×(1-1/3)2... × (1-1/n)n-1] × nn. I will then use this result and the definition of e^x since we are talking for...

Thanks for your response. So we have Tn+1 (x) = 2xTn(x) + Tn-1(x). So, the only thing to prove is that Tn-1(x) will be of degree k<n+1 (2xTn(x) will be of degree 1 + n by the assumption). This seems obvious, but still, how could I possibly prove it?

Homework Statement Let Tn(x)=cos(narccosx) where x is real and belongs to [-1,1] and n E Z+ Find T1(x). Show that T2(x)=2x^2 - 1. Show that Tn+1 (x) + Tn-1 (x) = 2xTn(x) Hence, prove by induction that Tn(x) is a polynomial of degree n. The Attempt at a Solution Since cosθ=x and arccosx=θ we...

Homework Statement So we have to prove that \frac{(n+1)(n+2)(n+3)...(2n)}{1*3*5...*(2n-1)} = 2n2. The attempt at a solution I. For n=1, obviously the proposition is true. (2*1/(2-1) = 2^1 = 2) II. Let n=k and assume \frac{(k+1)(k+2)(k+3)...(2k)}{1*3*5...*(2k-1)} = 2k. Now, for n=k+1 we...

A student stands on a bathroom scale in an elevator at rest on the 64th floor of a building. The scale reads 836 N. (a) As the elevator moves up, the scale reading increases to 936 N, then decreases back to 836 N. Find the acceleration of the elevator (ms^-2). (b) As the elevator approaches...