Which of the following series are geometric? Which are power ones? a) 1+x2+x24+x38+x416+… b) 1+1.1+1.21+1.331+1.4641+1.6105+… c) (13)2+(13)4+(13)6+(13)8+… d) 1+x+x22!+x33!+x44!+… e) 1+12+13+14+15+… f) 1x2+1x+1+x+x2+x3+x4+…

a) 1+x2+x24+x38+x416+… is both power and geometric series. b) 1+1.1+1.21+1.331+1.4641+1.6105+... is only power series c) (13)2+(13)4+(13)6+(13)8+… is geometric series. d) 1+x+x22!+x33!+x44!+… is geometric series. e) 1+12+13+14+15+… is neither geometric nor power one. f) 1x2+1x+1+x+x2+x3+x4+… is power series.

Best solutions to - "Which of the following series are geometric? Which..."

hexacordoK

Answered question

2021-08-16

Which of the following series are geometric? Which are power ones?
a)

1 + \frac{x}{2} + \frac{x^{2}}{4} + \frac{x^{3}}{8} + \frac{x^{4}}{16} + \dots

1 + 1.1 + 1.21 + 1.331 + 1.4641 + 1.6105 + \dots

{(\frac{1}{3})}^{2} + {(\frac{1}{3})}^{4} + {(\frac{1}{3})}^{6} + {(\frac{1}{3})}^{8} + \dots

1 + x + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + \frac{x^{4}}{4!} + \dots

1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \dots

\frac{1}{x^{2}} + \frac{1}{x} + 1 + x + x^{2} + x^{3} + x^{4} + \dots

Answer & Explanation

sweererlirumeX

Skilled2021-08-17Added 91 answers

a) $1 + \frac{x}{2} + \frac{x^{2}}{4} + \frac{x^{3}}{8} + \frac{x^{4}}{16} + \dots$ is both power and geometric series.
b) $1 + 1.1 + 1.21 + 1.331 + 1.4641 + 1.6105 + . . .$ is only power series
c) ${(\frac{1}{3})}^{2} + {(\frac{1}{3})}^{4} + {(\frac{1}{3})}^{6} + {(\frac{1}{3})}^{8} + \dots$ is geometric series.
d) $1 + x + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + \frac{x^{4}}{4!} + \dots$ is geometric series.
e) $1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \dots$ is neither geometric nor power one.
f) $\frac{1}{x^{2}} + \frac{1}{x} + 1 + x + x^{2} + x^{3} + x^{4} + \dots$ is power series.

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