About Introduction to Series:
A sequence as a function that computes an ordered list of numbers. When we add the terms of a sequence, we get a series. When we work with a series, we normally use the summation notation or the sigma notation.
Test Objectives
- Demonstrate the ability to evaluate a series
- Demonstrate the ability to work with summation notation
#1:
Instructions: Evaluate each series.
$$a)\hspace{.2em}\sum_{i=1}^{15}(3i - 4)$$
$$b)\hspace{.2em}\sum_{n=1}^{12}(8n - 12)$$
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#2:
Instructions: Evaluate each series.
$$a)\hspace{.2em}\sum_{n=1}^{5}(5n - 3)$$
$$b)\hspace{.2em}\sum_{i=1}^{10}(4i - 8)$$
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#3:
Instructions: Evaluate each series.
$$a)\hspace{.2em}\sum_{m=1}^{5}(5m + 5)$$
$$b)\hspace{.2em}\sum_{k=1}^{7}(2^{k - 1})$$
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#4:
Instructions: Evaluate each series.
$$a)\hspace{.2em}\sum_{m=1}^{9}(-4 \cdot 2^{m - 1})$$
$$b)\hspace{.2em}\sum_{i=1}^{7}(2 \cdot 5^{i - 1})$$
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#5:
Instructions: Evaluate each series.
$$a)\hspace{.2em}\sum_{k=2}^{5}(k + 1)^2(k - 3)$$
$$b)\hspace{.2em}\sum_{i=1}^{4}(3i^3 + 2i - 4)$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}300$$
$$b)\hspace{.2em}480$$
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#2:
Solutions:
$$a)\hspace{.2em}60$$
$$b)\hspace{.2em}140$$
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#3:
Solutions:
$$a)\hspace{.2em}100$$
$$b)\hspace{.2em}127$$
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#4:
Solutions:
$$a)\hspace{.2em}-2044$$
$$b)\hspace{.2em}39{,}062$$
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#5:
Solutions:
$$a)\hspace{.2em}88$$
$$b)\hspace{.2em}304$$
