Answered: 3. Determine whether the series… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 8E

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#3 part a

i can't remember how to determine the sum after finding conver

(d) lim ne-n²
818
(g) lim (√√n² +n− √√n²+1)
810
∞
(2) Σ
n=0
(d) Σ
n=1
2
4n² - 1
ANSWERS. (a) 12
(e) lim
81x
ANSWERS. (a) //
(b) 0
(c) 1
(d) 0
(e) ∞
(f) 0
(g) 1/1/2
3. Determine whether the series converges or diverges. If it converges, find its sum.
3n+1
∞
∞
(b)
5n
4n
(c) Σ(-1)"-1
3n-1
ANSWER.
(h) lim
16
11
n=0
n
(Inn)2
2n
n→∞ n!
(-3)^
5n+1
n
(e) Ein " (2+1)
n=1
(c) divergent
(d) 1
(b) /
(e)-o, divergent
4. Write the repeating decimal 1.45 = 1.4545454545 as a quotient of two integers
(f) lim
81x
...
(-1)" √n
n+1
n=1
(h
5. Determine whether the series converges or diverges. Give reasons for your answer.
1

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This solution was very helpful. I see the part I was missing was shifting the index from n=1 to n=0, so that it is possible to create the rational function in the form a/(1-r). Is there an easy procedure to go from n=1 to n=0 without working out the terms to see what the new sum is? I have seen the generalized procedure for shifting from any n to any other n, but is there a quick way to go from n=1 to n=0 for a power series?

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