Answer:
joe mama-
Step-by-step explanation:
a. Recall that
For 
, we have
By integrating both sides, we get
If 
, then
so that
We can shift the index to simplify the sum slightly.
b. The power series for 
can be obtained simply by multiplying both sides of the series above by 
.
c. We have
Now that we’ve learned how to solve word problems involving the sum of consecutive integers, let’s narrow it down and this time, focus on word problems that only involve finding the sum of consecutive even integers.
But before we start delving into word problems, it’s important that we have a good understanding of what even integers, as well as consecutive even integers, are.
Even Integers
We know that even numbers are integers that can be divided exactly or evenly by 22. Thus, the general form of the even integer nn, is n = 2kn=2k, where kk is also an integer.
In other words, since even numbers are the multiples of 22, we can represent an even integer nn by 2k2k, where kk is also an integer. So if we have the even integers 1010 and 1616,
