Question

I do not understand a problem from a text book or how to solve the problem for the answer. Could shomeone show me the steps (show work) on how to solve this question.

The sum of the intergers from 1 through n is n(n+1)/2. the sum of the squares of the intergers from 1 through n is n(n+1)(2n+1)/6. The sum of the cubes of the integers from 1 through n is n squared(n+1)squared/4. Use the appropriate expressions to find the following values.
(A). The sum of the integers from 1 through 30.
(B) The sum of the squares of the integers from 1 through 30
(C) The sum of the cubes of integers from 1 through 30.
(D) The square of the sum of the integers from 1 though 30.
(E) The cube of the sum of integers from 1 through 30.
I's sure its much easier than what I am making it out to be. I tried working the problems but am lost in what it' asking.

Answer 1

They have given you the formulas for each of the question for A, B, and C

I will do B
Sum of squares from 1 to n
= n(n+1)(2n+1)/6
so the sum of the squares from 1 to 30, n=30
just plug it in
sum of squares = 30(31)(61)/6 = 9455

do A and C the same way

Once you have the answer for A,
square that result for D
cube the result for A to get E

Answer 2

During a walk, Dave completed the first two miles at a pace of 3mph. He walked the next two miles at a pace of 4.5 mph. Would his walk take more, less or the samr time if he walked the entire distance of four miles at a steady pace of 3.5 mph?