What is the ratio for this ? 2:25
2 answers:
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Answer:
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.