Answer:
The proof is shown in the explanation below.
Step-by-step explanation:
Analysis:
The proof by induction focuses on n. In this case, let n = 1, and
will be a linear operator since
The exercise will show that
is a linear operator on V and that
is also a linear operator on V. This, follows that:

Answer:

Step-by-step explanation:
Given:
To find:
- Summation notation of the given series
Summation Notation:

Where n is the number of terms and
is general term.
First, determine what kind of series it is, there are two main series that everyone should know:
A series that has common difference.
A series that has common ratio.
If you notice and keep subtracting the next term with previous term:
Two common difference, we can in fact say that the series is arithmetic one. Since we know the type of series, we have to find the number of terms.
Now that brings us to arithmetic sequence, we know that first term is 5 and last term is 251, we’ll be finding both general term and number of term using arithmetic sequence:
<u>Arithmetic Sequence</u>

Where
is the nth term,
is the first term and
is the common difference:
So for our general term:

And for number of terms, substitute
= 251 and solve for n:

Now we can convert the series to summation notation as given the formula above, substitute as we get:

Answer:
3.5 times 2 equals 7 so try 2.5 times 2 which would be 5, 5 could be the answer but im not sure :)
Answer:
<h3>2min/customer</h3>
Step-by-step explanation:
If 8 customers entered a store over the course of 16 minutes, then;
8 customers = 16 minutes.
The rate at which the customers are entering is expressed as;
Rate = Time (in minutes)/amount of customers;
Given
Time = 16 minutes
Amount of customers = 8 customers
Rate = 16min/8customers
Rate = 2min/customer
Hence the rate at which the customers entering the store in minutes per customer is 2min/customer.