Given:
When establishing the internet service, there was an initial fee as well as a monthly fee on the contract.
The given function is:
To find:
The cost of internet service if they began service in March 2020.
Solution:
We have,
We need to find the internet service cost for the first month. So, substitute in the given function.
Therefore, the cost of internet service is 75 if they began the service in March 2020.
Let
In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:
So, the base case is ok. Now, we need to assume and prove
.
states that
Since we're assuming , we can substitute the sum of the first n terms with their expression:
Which terminates the proof, since we showed that
as required