Coding in R:

We are interested in calculating only the sum of the even powers: h(x,n) = 1 + x^2 + x^4 + ... + x^(2*floor(n/2)), where floor(n/2) is the largest whole number smaller than n/2, that 2*floor(n/2) is the largest even number smaller than n.

a) Write a function to calculate this: hn.skip(x,n,skip=2)

b) Use the skip argument in hn.skip to sum up 1 + x^s + x^(2s) + ... for any integer s.