Calculate the sum of the series ∑∞n=1 a n whose partial sums are given. sn=2−3(0.8)n

Determine the maximum&nbsp;sn&nbsp;as&nbsp;n→∞&nbsp;limn→∞[2−3(0.8)n]=2−limn→∞3(0.8)n=2−0=2&nbsp;(0.8)n&nbsp;becomes tiny as&nbsp;n→∞, so -3 times that will approach 0.&nbsp;sn=2&nbsp;as&nbsp;n→∞&nbsp;Result:&nbsp;sn=2&nbsp;as&nbsp;n→∞

Answered: "Calculate the sum of the series ∑∞n=1 a..."

College
Calculus and Analysis
Differential Calculus
Limits and continuity

iohanetc

Answered question

2021-10-25

Calculate the sum of the series

\sum \infty n = 1

a n whose partial sums are given.

s n = 2 - 3 {(0.8)}^{n}

Answer & Explanation

crocolylec

Skilled2021-10-26Added 100 answers

Determine the maximum $s_{n} a s n \to \infty$
$lim_{n \to \infty} [2 - 3 {(0.8)}^{n}] = 2 - lim_{n \to \infty} 3 {(0.8)}^{n} = 2 - 0 = 2$
${(0.8)}^{n}$ becomes tiny as $n \to \infty$ , so -3 times that will approach 0.
$s_{n} = 2 a s n \to \infty$
Result:
$s_{n} = 2 a s n \to \infty$

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