Sequences And Series Of Real Numbers -8 - Mathematics MCQ

convergent

divergent

oscillating finitely

oscillating infinitely

p > 1

P < 1

p ≤ 1 

p = 1

{a_n} converges to zero and {b_n} is Cauchy sequence

{a_n} converges to zero and {b_n} is not a convergent sequence

{a_n} converges to a non-zero number and {b_n} is a Cauchy sequence

{a_n} converges to a non-zero number and {b_n} is not a convergent sequence

convergent

divergent

oscillatory

None of these

1

e

1/e

4/e

the sequence   is convergent and is not convergent

the sequence diverges to ∞

the sequence does not converges to 0

the sequence converges to 0 

converges to 1

converges to a number > 1

diverges to ∞

has an oscillating sequences of partial sums

convergent

divergent

oscillating infinitely

oscillating finitely

0

1

e

None of these

Convergent

Divergent

Neither convergent no divergent

None of these

∑q_n may be convergent if ∑a_n is conditionally convergent

∑p_n or ∑q_n is divergent then ∑a_n is divergent

∑a_n is absolutely convergent if ∑P_n and ∑q_n are convergent. But converse may be true

∑a_n is absolutely convergent then ∑p_n and ∑q_n are convergent

0

1

2

log_e2

 exists

 may exist

 does not exists

 exist infinitely

t > 1/3

t > 1/2

 t > 1

t > 3/2

1

0

e

None of these

r < 1

r > 1

r = 1

r = -1