Isn't the force of gravity just a result of the shape of space as it is affected by masses within it? Why is it believed that it is a force associated with theoretical force particles "gravitons"? I can understand that the electric or magnetic force is a product of particles with fundamental...
Homework Statement
Find the formula of the partial sum of the series Ʃ1/[k(k+2)] k from 1 to infinity
Homework Equations
The Attempt at a Solution
Using partial fractions i rewrite the series as 1/2*Ʃ[1/k] - [1/(k+2)]
Then I start writing out the series from k=1 to 5...
Telescoping series
Ok I have read a bit on telescoping series. One thing I do not understand is this:
Why does it go from 1/[k(k+2)] to 1/k - 1/k+2, why are they subtracted instead of added?
Homework Statement
Consider the series Ʃ 1/[k(k+2)]; n=1 to infinity
Find the formula for the partial sum Sn
2. The attempt at a solution
I have calculated the first 5 terms of the sequence as follows, but I can't see any pattern. Am I doing this right?
S1=1/3
S2=1/3+1/8=11/24...