The answer I got for question 1 was: 3[( n (n+1) (2n+1) ) / 6]

Is that correct or no? Just a confirmation.

Please answer question 2.

I know this may seem like a math problem, but this is actually a computer science problem concerning algorithms, specifically summation approximation.

1. Consider k=1n3k2. Simplify the sum to obtain the exact polynomial? You may do this any way you like Do not use integrals for this problem. Do not worry about floors and ceilings (so you may assume that n is "nice"). Ignore second order terms. Consider k=1n3k2. (a) Split the sum into two equal-sized regions to obtain an upper bound for its value. (b) Split the sum into two equal-sized regions to obtain a lower bound for its value (as done in class). (c) Show how to obtain a better upper bound by splitting the sum into two unequal-sized regions. Make your bound as tight as possible. How does your bound compare with the upper bound obtained in Part (a)? (d) Show how to obtain a better lower bound by splitting the sum into two unequal-sized regions. Make your bound as tight as possible. How does your bound compare with the lower bound obtained in Part (b)