hw-11-03-integral-test

# hw-11-03-integral-test - If not explain how else you might...

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Chapter 11.3 homework: Integral Test The usual even/odd policy applies. Drill: #5 sum 1/(2n+1)^3 #7 sum n*e^(-n) #9 sum 2/n^0.85 #11 1+1/8 + 1/27 + 1/64 + . .. #12 1+1/(2 sqrt(2)) + 1/(3 sqrt(3)) + . .. #13 1+ 1/3 + 1/5 + 1/7 + . .. #14 1/5 + 1/8 + 1/11 + 1/14 + . .. #29 sum n*(1+n^2)^p #30 sum ln(n) / n^p Question A: If your computer summed terms of the Harmonic series at a rate of 1 billion per second (10^9 per second), what would its sum be (roughly) after a day of summing? Question B: i) Consider the sum of e^-n; is it a Geometric series? If so, compute its sum (n=1 to infinity).
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Unformatted text preview: If not, explain how else you might attack it. ii) Consider the sum of n^-e; is it a Geometric series? If so, compute its sum (n=1 to infinity). If not, explain how else you might attack it. Question C: Consider the sum (n=0 to infinity) of (sin(pi*n))^2. i) Does the sum converge? Explain. ii) Does the integral converge? Explain. (you do not have to find the actual value of the integral--a graph will help you find a shortcut) iii) How does the Integral Test apply or fail to apply here? Explain....
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