Hello. I'm stuck on another proof. Can anyone help me with this problem?
Let S of N be the Nth partial sum of the harmonic series
a) Verify the following inequality for n=1,2,3. Then prove it for general n.
+ + + ... +
b) Prove that S diverges by showing that for N=
Hint: Break up Sn into n+1 sums of length 1,2,4,8..., as in the following:
S of = 1 + (1/2) + (1/3 + 1/4) + (1/5 + 1/6 + 1/7 + 1/8)