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...

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

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