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Consider the following sum (which is in expanded form): 1−4 + 7−10 + 13−16 + 19−22...

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Advance Math

Consider the following sum (which is in expanded form): 1−4 +7−10 + 13−16 + 19−22 +···±(3n−2).

Note that this is slightly different from the previous sum inthat every other term is negative.

(a) Write it as a summation (∑).

(b) Evaluate the sum for every integer n from 1 to 9. (Becareful - if you get this wrong, you will likely get the rest ofthis question wrong!)

(c) Write a closed-form formula for the value of the sum as afunction of n. As in problem 1, do not use a \"by cases\" orpiecewise definition (will need to write a single closed-formexpression to receive full credit).(Hint 1: floor and ceilingfunctions may be useful here.)(Hint 2: try splitting up thesequence of partial sums into two subsequences, finding formulasforeach of the subsequences, then combining the formulas.)

(d) Prove that your formula from part (c) is correct usingMathematical Induction. (You may separateout the cases whereniseven/odd if you wish, but if so please do it as late aspossible.)

i. State and prove the Base Case.

ii. State the Inductive Hypothesis.

iii. Show the Inductive Step

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