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Question
Answer the following:
Find `sum_("r" = 1)^"n" (5"r"^2 + 4"r" - 3)`
Solution
`sum_("r" = 1)^"n" (5"r"^2 + 4"r" - 3)`
= `5sum_("r" = 1)^"n" "r"^2 + 4sum_("r" = 1)^"n""r" - 3sum_("r" = 1)^"n" 1`
= `5*("n"("n" + 1)(2"n" + 1))/6 + 4*("n"("n" + 1))/2 - 3"n"`
= `"n"/6[5(2"n"^2 + 3"n" + 1) + 12("n" + 1) - 18]`
= `"n"/6(10"n"^2 + 27"n" - 1)`.
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