Useful Summation Formulas (which can be proven by induction): Sum of the first n positive integers: sigma_i = 1^n i = 1 + 2 + 3 +

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Useful Summation Formulas (which can be proven by induction): Sum of the first n positive integers: sigma_i = 1^n i = 1 + 2 + 3 + ... + n = n(n + 1)/2 Sum of the square of the first n positive integers: sigma_i = 1^n i^2 = 1^2 + 2^2 + 3^2 + ... + n^2 = n)n + 1) (2n +1)/6 Sum of the cubes of the first n positive integers: sigma_i = 1^n i^3 = 1^3 2^3 + 3^3 + ... + n^3 = (n(n +1)/2)^2 Consider sigma_i = 1^n (10i/n - 3) 4/4. (a) Use the formulas to assist in finding the value of sigma_i = 1^n (10i/n - 3)4/4 as an expression involving n. Show work. Simplify your result as much as possible. b). Take the limit of your answer for (a) as n rightarrow infinity. What is the value of the limit?