Question

Find a general term (as a function of the variable n) for the
sequence{?1,?2,?3,?4,…}={45,1625,64125,256625,…}{a1,a2,a3,a4,…}={45,1625,64125,256625,…}.

Find a general term (as a function of the variable n) for the
sequence {?1,?2,?3,?4,…}={4/5,16/25,64/125,256/625,…}

an=

Determine whether the sequence is divergent or convergent. If
it is convergent, evaluate its limit.

(If it diverges to infinity, state your answer as inf . If it
diverges to negative infinity, state your answer as -inf . If it
diverges without being infinity or negative infinity, state your
answer as div )

lim?→∞[ln(?+1)−ln(?)]

Determine whether the sequence is divergent or convergent. If
it is convergent, evaluate its limit. If it diverges to infinity,
state your answer as INF. If it diverges to negative infinity,
state your answer as MINF. If it diverges without being infinity or
negative infinity, state your answer as DIV.

lim?→∞6?^3+sin^2(5?)/?^4+15

Determine whether the sequence is divergent or convergent. If
it is convergent, evaluate its limit. If it diverges to infinity,
state your answer as INF. If it diverges to negative infinity,
state your answer as MINF. If it diverges without being infinity or
negative infinity, state your answer as DIV.

lim?→∞. n^n/e^6n

Answer #1

. A sequence { bn } is defined recursively bn= -bn-1/2, where b1
= 3. (a) Find an explicit formula for the general term of the bn =
f(n). (b) Is the sequence convergent or divergent? (c) Consider the
series ∑ approaches infinity and n=1 bn. Is this series
convergent or divergent? (d) If it is convergent, find its sum

Consider the series ∑n=1 ∞ an
where
an=(5n+5)^(9n+1)/
12^n
In this problem you must attempt to use the Ratio Test to decide
whether the series converges.
Compute
L= lim n→∞
∣∣∣an+1/an∣∣
Enter the numerical value of the limit L if it converges, INF if
the limit for L diverges to infinity, MINF if it diverges to
negative infinity, or DIV if it diverges but not to infinity or
negative infinity.
L=
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