INFINITE SERIES
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How to prove the sequence (an) does not converge?

a_{n =1+1/2+1/3+...+1/n}

A(N)=1+(1/2)+(1/3)+(1/4)+(1/5)+(1/6)+(1/7)+1/8)+…...……..
A(N)=1+(1/2)+[(1/3)+(1/4)]+[(1/5)+(1/6)+(1/7)+1/8)]+…...……..
OBVIOUSLY A(N) > B(N ) WHERE B(N) IS
B(N)=1+(1/2)+[(1/4)+(1/4)]+[(1/8)+(1/8)+(1/8)+1/8)]+…...……..
B(N)=1+(1/2)+[1/2]+[1/2]+…… = 1+(1/2)+(N/2)
CLEARLY AS N TENDS TO INFINITY B(N) TENDS TO INFINITY .
BUT A(N) > B(N)……SO A(N) TENDS TO INFINITY
THAT IS THE SEQUENCE A(N) IS DIVERGENT …PROVED…