Sequences and Series : Explicit Rule and Recursive Rule; Integrals and Exponential Growth
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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.
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Solution Summary
Sequences and series, explicit rule and recursive rule and integrals and exponential growth are investigated in the solution.
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"
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