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Section 1.3

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1. (a) \displaystyle{\sum_{n=1}^\infty \left(\frac{1}{3}\right)^{n-1} = \frac{3}{2}}

(c) \displaystyle{\sum_{n=1}^\infty \left(\frac{2}{5^n}\right) = \frac{1}{2}}

(e) \displaystyle{\sum_{n=1}^\infty 7\left(\frac{1}{3}\right)^n\frac{2}{5}^{n-1} = \frac{35}{13}}

(g) Does not converge

(i) Does not converge

(k) Does not converge

(m) \displaystyle{\sum_{n=1}^\infty \sin(n\pi) = 0}

(n) Does not converge

3. (a) \pi

(b) 99

5. (a) 10 billion dollars

(c) \dfrac{A}{1 - r} dollars

7. 70 meters; \dfrac{50}{3} meters

9. \dfrac{4}{9}

11. 83 terms for a partial sum larger than 5 ; 12,367 terms for a partial sum larger than 10

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