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# Sequences and Series : Explicit Rule and Recursive Rule; Integrals and Exponential Growth

1.) For the arithmetic sequence {-10,-2,6,14,}, find:
a.) a recursive rule for the nth term
b.) an explicit rule for the nth term
2.) For the geometric sequence {512,256,128,64,...}, find:
a.) a recursive rule for the nth term
b.) an explicit rule for the nth term
3.) Determine whether each of the following sequences converges or diverges. If it converges, find its limit.
a.) a= (5+2n)/(n^2)
b.) a= (-1)^n(1.001)^n
4.) Which grows faster as x approaches infinity, lnx or x^3?
a.) lnx grows faster b.) x^3 grows faster c.) they grow at the same rate
5.) Which grows faster as x approaches infinity, (x-4)^3 or 2x^3+lnx?
a.) (x-4)^3 grows faster b.) 2x^3+lnx grws faster c.) they grow at the same rate
6.) Evaluate the integral from 0 to infinity of (dx)/((1+x)(square root of x)) or state that it diverges.
7.) Use partial fractions to evaluate the integral of (20x+16)/(x^2+3x+2)dx.

#### Solution Summary

Sequences and series, explicit rule and recursive rule and integrals and exponential growth are investigated in the solution.

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