a) what distinguishes convergent sequences from divergent sequences

• Convergent sequences have a finite limit.

Example

1,1/2,1/3,1/4….1/n   limit=o

• Divergent sequences do not have a finite limit.

Example

1,3,5,7,9…2n-1   limit=infinite

b) what distinguishes convergent series from divergent series

• The Comparison Test

Let X n≥1 an and X n≥1 bn be series with all positive terms.

(a) If X n≥1 bn converges and an ≤ bn for all n, then X n≥1 an converges.

(b) If X n≥1 bn diverges and an ≥ bn for all n, then X n≥1 an diverges.

• The Limit Comparison Test

Let X n≥1 an and X n≥1 bn be series with all positive terms.

If limn→∞ an bn = L > 0,

then both series converge or both series diverge.