Consider the sequence {an} = {nrn}. Decide whether {an} converges for each value of r. (a) r = 1/5
(b) r = 1
(c) r = 1/6
For what values of r does the sequence {nr^n} converges?

a). converges

b). diverges

c). converges

Step-by-step explanation:

{ } = { }

Using radio test,

L =

   =

   =

   =

   = |r|

Therefore, converges in |r| < 1

a). r = 1/5

This sequence is monotonically decreasing and bounded.

0 < < 1

Hence, { } converges.

b). r = 1

    { } = { n }

This sequence is monotonically increasing sequence which is not bounded.

Hence, { } diverges.

c). r = 1/6

This sequence is monotonically decreasing and bounded.

0 < < 1

Hence, { } converges.

For  |r| < 1, the converges.

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i think it’s c i believe