Summation Properties and Rules — Quiz

Question 9 • Precalculus

Which of the following shows one way to simplify this expression? the sum from n is equal to 1 to 43 of open paren 3 plus 9 close paren

Answer

the sum from n is equal to 1 to 43 of open paren 3 plus 9 close paren 3 the sum from n is equal to 1 to 43 of 9 27 the sum from n is equal to 1 to 43 of n

the sum from n is equal to 1 to 43 of open paren 3 plus 9 close paren the sum from n is equal to 1 to 43 of 3 3 the sum from n is equal to 1 to 43 of open paren 1 plus 3 close paren 3 the sum from n is equal to 1 to 43 of 1 plus the sum from n is equal to 1 to 43 of 3 3 the sum from n is equal to 1 to 43 of 1 plus 3

the sum from n is equal to 1 to 43 of open paren 3 plus 9 close paren the sum from n is equal to 1 to 43 of 3 plus the sum from n is equal to 1 to 43 of 9 the sum from n is equal to 1 to 43 of 3 plus 9

the sum from n is equal to 1 to 43 of open paren 3 plus 9 close paren the sum from n is equal to 1 to 43 of 3 plus the sum from n is equal to 1 to 43 of 9 the sum from n is equal to 1 to 43 of 3 plus the sum from n is equal to 1 to 43 of 9 plus the sum from n is equal to 1 to 43 of n

Explanation

Use the sum rule that the sum of two terms can be split into the sum of each term: ∑ₙ₌₁⁴³(3 + 9) = ∑ₙ₌₁⁴³3 + ∑ₙ₌₁⁴³9. Choice C shows this split. Both sums have the same limits, from 1 to 43.

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