Question

Determine the sum of the series if it exists. Give the sum as an integer r reduced fraction if the series converges. Enter DNE if it the series diverges. $$ \sum_{k=0}^{\infty} 3 \cdot \left(\frac{2}{5}\right)^k = $$

Name: determine the sum of the series if it exists give the sum as an integer r reduced fraction if the series converges enter dne if it the series diverges sumk0infty 3 cdot leftfrac25rightk 46398
Uploaded: 2020-05-31T21:11:16-08:00
Duration: 54 s
Channel: Linh Vu
Description: determine the sum of the series if it exists give the sum as an integer r reduced fraction if the series converges enter dne if it the series diverges sumk0infty 3 cdot leftfrac25rightk 46398

          Determine the sum of the series if it exists. Give the sum as an integer r reduced fraction if the series converges. Enter DNE if it the series diverges.
$$ \sum_{k=0}^{\infty} 3 \cdot \left(\frac{2}{5}\right)^k = $$

$determine the sum of the series if it exists give the sum as an integer r reduced fraction if the series converges enter dne if it the series diverges sumk0infty 3 cdot leftfrac25rightk 46398$

Added by Robert S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Linh Vu

05/31/2020

Step 1

In this case, $a = 3$ and $r = \frac{2}{5}$. Step 2: A geometric series converges if $|r| < 1$. Here, $r = \frac{2}{5}$, so $|r| = \left|\frac{2}{5}\right| = \frac{2}{5}$. Since $\frac{2}{5} < 1$, the series converges. Step 3: The sum of a convergent geometric Show more…

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Determine the sum of the series if it exists. Give the sum as an integer r reduced fraction if the series converges. Enter DNE if it the series diverges. $$ \sum_{k=0}^{\infty} 3 \cdot \left(\frac{2}{5}\right)^k = $$