Calculus practice
Summation Properties worksheets
Evaluate finite sums with linearity, supplied sums, constant sums, and power-sum formulas through cubes.
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Use summation properties to evaluate each of twelve sums. Show the property and substitutions.
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What this activity builds
Separate sums, factor out coefficients, and use the correct lower and upper bounds.
Worked example
If the sum of u(i) from i=2 to5 is10, what is the sum of 3u(i)+2 over those bounds?
3(10) + 2(4) = 38.
Take the coefficient outside the sum. There are 5-2+1=4 constant terms.
Teaching notes
Make the practice count
- Keep the same bounds when splitting a sum.
- For a lower bound above1, subtract the prefix ending at lower-1.
- The index letter does not change the value.
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Twelve sums combine supplied totals, constant sums, and powers through cubes. Choose one index letter or mix letters between problems.