Evaluate the factorial expression. (n+4)! n+4

The simplified form of given factorial expression is (N+3)!.

Step-by-step explanation:

The given expression is

The n! is defined as

The given expression can be written as

Cancel out the common factors.

Therefore the simplified form of given factorial expression is (N+3)!.

answer: the area of the parallelogram below is 42 square meters.

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, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for