Series And Sequences

Question 1

Nth term

Answer 1

Take the lim x approaches infinity. If =0 converge, if not=0 diverge

Question 2

Harmonic

Answer 2

1/n always siverge

Question 3

Telescoping

Answer 3

Partial fractins

Question 4

Geometric series (number raised to a variable)

Answer 4

r^n |r|<1 conveges

Question 5

P series

Answer 5

1/n^p. P>1 converge

Question 6

Alternating series

Answer 6

(-1)^n(x) take out the (-1)^n and take lim as x approaches infinity lim =0 converge

Question 7

Direct comparison

Answer 7

Choose a pseries or geometric that original is close to- maybe simplifies to

Question 8

Limit comparison

Answer 8

Lim x approaches infinity (original/comparison) comparison converges and lim greater than 0 converge

Question 9

Ratio test

Answer 9

Lim x approaches infinity | a(n+1)/a(n) |. Lim less than 1 absolutely convergent