1) Leta_k=k2+sink7k. Which of the following inequalities is/are true for any positive integer k?

Select all that apply.

ak>7/k

0

ak7kk2+1

02+1

0

2)Letan be an infinite series.

Choose the correct statements below.

If an converges, then |an| converges.

If |an| converges, then an converges.

If an diverges, then |an| diverges.

If |an| diverges, then an diverges.

3) The seriesn=1n4cos(n) converges absolutely. What does that mean?

n=1n4cos(n)diverges

n=1n4cos(n)converges

Bothn=1cos(n) andn=1n41

There is a very high chance thatn=1n4cos(n)converges.