1. Show that each series is divergent 2. Find the sum of each series. 3. Given the series a n and b n , suppose that there exists a natural number N such that a n = b n for all n  N. Prove that a n is...

1. Show that each series is divergent

2. Find the sum of each series.

3. Given the series
a_n
and
b_n, suppose that there exists a natural number N such that a_n
= b_n
for all n
 N. Prove that
a_n
is convergent iff
b_n
is convergent. Thus the convergence of a series is not affected by changing a finite number of terms. (Of course, the value of the sum may change.)