Chapter 12: Q 12.52 (page 1191)

Find the sum:
$\sum_{i = 1}^{10} 5 {(2)}^{i}$

Short Answer

Expert verified

The sum is equal to $10230$

Step by step solution

Step 1. Given information

It is given that $\sum_{i = 1}^{10} 5 {(2)}^{i}$ .

Step 2. Find the sum.

Consider $\sum_{i = 1}^{10} 5 {(2)}^{i}$

Let $a, r$ denote the first term and common ratio respectively.

role="math" localid="1645371460934" $\begin{array}{rcl} a & = & 5 {(2)}^{1} \\ = & 10 \\ r & = & \frac{5 {(2)}^{i + 1}}{5 {(2)}^{i}} \\ = & 2 \end{array}$

So,

$S_{n} = \frac{a (1 - r^{n})}{1 - r}$ where $S_{n}$ is the sum.

$\begin{array}{rcl} S_{10} & = & \frac{10 (1 - 2^{10})}{1 - 2} \\ = & - 10 (1 - 1024) \\ = & 10230 \end{array}$

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Find the sum:
$\sum_{i = 1}^{10} 5 {(2)}^{i}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the sum.

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Find the sum:∑i=11052i

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the sum.

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Find the sum:
$\sum_{i = 1}^{10} 5 {(2)}^{i}$