Page:Elements of the Differential and Integral Calculus - Granville - Revised.djvu/250

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 * 23.
 * $$ \frac{\cos x}{e^x} + \frac{\cos 2x}{e^{2x}} + \frac{\cos 3x}{e^{3x}} + \cdots.$$
 * Ans. $$x>0.$$.
 * align="center" | [[Image:Wag-142-7-Interval_Of_Convergence.png‎|Wag-142-7 Interval of Convergence]]
 * colspan=3| Neither the sine nor cosine can exceed 1 numerically.
 * 24.
 * $$ 1 + x \log a + \frac{x^2\log^2a}{2!} + \frac{x^3\log^3a}{2!} + \cdots.$$
 * Ans. All values of $$x$$.
 * align="center" | [[Image:Wag-142-6-Interval_Of_Convergence.png‎|Wag-142-6 Interval of Convergence]]
 * 25.
 * $$ \frac{1}{1+x} + \frac{1}{1+x^2} + \frac{1}{1+x^3} + \cdots.$$
 * Ans. $$x >1.$$
 * align="center" | [[Image:Wag-142-8-Interval_Of_Convergence.png‎|Wag-142-8 Interval of Convergence]]
 * 26.
 * $$ x +\frac{1}{2}\cdot\frac{x^3}{3} +\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{x^5}{5} + \frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot\frac{x^7}{7} + \cdots.$$
 * Ans. $$-1 \le x \le 1.$$
 * align="center" | [[Image:Wag-142-9-Interval_Of_Convergence.png‎|Wag-142-9 Interval of Convergence]]
 * 27.
 * $$ 1 + x +2x^2 + 3x^3 + \cdots.$$
 * 28.
 * $$ x - \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7} + \cdots.$$
 * 29.
 * $$ 10x + 100x^2 + 1000x^3 + \cdots.$$
 * 30.
 * $$ 1 +x + (2!)x^2 + (3!)x^3 + \cdots.$$
 * }
 * 28.
 * $$ x - \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7} + \cdots.$$
 * 29.
 * $$ 10x + 100x^2 + 1000x^3 + \cdots.$$
 * 30.
 * $$ 1 +x + (2!)x^2 + (3!)x^3 + \cdots.$$
 * }
 * 29.
 * $$ 10x + 100x^2 + 1000x^3 + \cdots.$$
 * 30.
 * $$ 1 +x + (2!)x^2 + (3!)x^3 + \cdots.$$
 * }
 * 30.
 * $$ 1 +x + (2!)x^2 + (3!)x^3 + \cdots.$$
 * }
 * }
 * }
 * }