Final answer:
The sum of the expression from k = 1 to k = 100 of k^2 + k + 1 is calculated using the formulas for the sum of squares and the sum of natural numbers, then combining these with the additional constant terms included in the series.
Step-by-step explanation:
The question involves calculating the sum from k = 1 to k = 100 of the expression k^2 + k + 1. To calculate this, we can use the formulas for the sum of the first n squares and the sum of the first n natural numbers. The sum of the first n squares is given by (n)(n + 1)(2n + 1)/6, and the sum of the first n natural numbers is given by (n)(n + 1)/2. Adding these and including the n terms of the '+1' from the original expression, we get the total sum.
To illustrate, the calculation of the sum of squared errors (SSE) in the provided statistics example uses the concept of squaring each term and adding them together.
Similarly, we will calculate the sums of k^2, k, and the constant term separately and then combine them to find the final answer. Calculate the sum of the squares of k, the sum of k, and add 100 for the '+1' added 100 times (since there are 100 terms).