- #1
ThomasR
- 2
- 0
Hello
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.
Cheers
Tom
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.
Cheers
Tom