Question

If am, bm, and cm satisfy the inequalities 0 < bm < Cm < am , for all m, what can we say about the

[infinity][infinity]
(A)Σam(B)Σbm
m=1m=1
series if we know that the series
[infinity]
(C)Σcm
m=1
is divergent but know nothing else about am and bm?
1. (A) diverges , (B) diverges
2. (A) diverge, (B) converges
3. (A) converges, (B) need not converge
4. (A) converges, (B) diverges
5. (A) need not diverge. {B) diverges
6. (A) diverges, (B) need not diverge

Answer 1

6. (A) divergent, (B) need not divergent

Explanation:

using comparision test, A is divergent since it is greater than a divergent series but we don't know if B is divergent since it is less than divergent series but we don't know if it is converget either.