Register to reply

Sums of series for Riemann integrals

by ThomasR
Tags: integrals, riemann, series, sums
Share this thread:
May25-07, 02:28 AM
P: 2

I'm having some difficulty in finding sums which relate to Riemann integrals.

The first one seems pretty simple.. a finite calculation of what would otherwise be the harmonic series i.e. 1/k from k=n to k=(2n-1). I can't see an easy way of finding a formula in terms of n, however.

The second one is similar.. sum of k/[n(k+n)] from k=1 to k=n. Again, completely stumped here as to how to get it into a nice format.

Finally, I need to sum from k=1 to k=(n-1) the values of sin(k*pi/2n). I have a similar result for cos(k*pi/2n) and it mentions using trigonometric/geometric series (which I presume means using the fact that sin(k*pi/2n) = Im(e^i(k*pi/2n)) but am unsure where to go from here.

Help on any of the above would be appreciated .. or just some general approach.

Phys.Org News Partner Science news on
New type of solar concentrator desn't block the view
Researchers demonstrate ultra low-field nuclear magnetic resonance using Earth's magnetic field
Asian inventions dominate energy storage systems

Register to reply

Related Discussions
Riemann sums Calculus & Beyond Homework 34
Riemann sums Calculus & Beyond Homework 1
Log and Riemann sums Calculus 10
Riemann sums question Calculus 4
Riemann Sums Calculus 3