compare some functions

Question

Assume that I have three function:

sum1[n_] := Sum[Cos[k/n], {k, 0, n}]
sum2[n_] := Sum[Sin[k/n], {k, 0, 2n}]
sum3[n_] := Sum[Cos[k + 1/2n], {k, 0, 2n - 1}]

For each $n<100$, how can I compare these three function?

For example Mathematica tells me sum2[3]> sum1[3]>sum3[3] or sum3[5]>sum[5]>sum1[5].

And @@ Table[sum2[n] > sum1[n] > sum3[n], {n, 1, 100}] evaluates to True — Bob Hanlon, Oct 05 '17 at 14:40

score 1 · Answer 1 · answered Oct 05 '17 at 13:40

1

DiscretePlot[{sum1[n], sum2[n], sum3[n]}, {n, 1, 100}]

answered Oct 05 '17 at 13:40

kiara

Better still, plot the differences – Lotus Oct 05 '17 at 14:13
Plot doesn't work good for large domains. Isn't there any way else?or only way is that I must use several If? – A. Mpi Oct 05 '17 at 15:10

1 Answers1