Chapter 12: Q. 323 (page 1222)

Expand the partial sum and find its value. ${\sum {(- 4)}^{i}}_{i = 1}^{4}$

Short Answer

Expert verified

The value of the partial sum ${\sum {(- 4)}^{i}}_{i = 1}^{4}$ is $204$

Step by step solution

Step 1. Given

The partial sum is ${\sum {(- 4)}^{i}}_{i = 1}^{4}$

To find the value of partial sum.

Step 2. Substitute the values and expand the partial sum.

Substitute the values of $i$ from $1$ and expand them.

${\sum {(- 4)}^{i} =}_{i = 1}^{4} {(- 4)}^{1} + {(- 4)}^{2} + {(- 4)}^{3} + {(- 4)}^{4}$

Step 3. Find the values of expanded term

${\sum {(- 4)}^{i}}_{i = 1}^{4} = (- 4) + 16 + (- 64) + 256 = 204$

The value of partial sum is $204$

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Expand the partial sum and find its value. ${\sum {(- 4)}^{i}}_{i = 1}^{4}$

Short Answer

Step by step solution

Step 1. Given

Step 2. Substitute the values and expand the partial sum.

Step 3. Find the values of expanded term

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Expand the partial sum and find its value. ∑(-4)ii=14

Short Answer

Step by step solution

Step 1. Given

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Expand the partial sum and find its value. ${\sum {(- 4)}^{i}}_{i = 1}^{4}$