
Simplify the following factorial expression:
Answer
477.9k+ views
Hint:We have to simplify the factorial expression given in the fractional form. We use the definition of factorial of that is given by the formula
and use it to solve the problem.
Complete solution step by step:
Firstly we write the expression given in the question
Now, we use the definition of factorial to see how we can expand the factorials of both numerator and denominator i.e.
We can see that factorial of a number is product of all integers starting from 1 to that number so we can expand the given values in our question like this
Now we put these values in the given equation (1) to see how we can proceed
Now we see that that both in denominators we have the expansion of so we write it as
Now we can cancel the terms like this
So we have simplified the fraction in this form.
Additional information: We can check our answer by putting a value of in the expression and solve it then we check if it is the same when the substitution is made in the result expression i.e.
Let so we have
And now putting the same value in the RHS
So we have obtained the same answer by putting the value of ‘n’.
Note: Knowing properties of factorials helps us in this problem. Factorials can be represented in two ways by putting an exclamation mark (!) after an expression or by putting the number in an ‘L’ shaped symbol. Both the notations are correct and acceptable by the math fraternity.
Complete solution step by step:
Firstly we write the expression given in the question
Now, we use the definition of factorial to see how we can expand the factorials of both numerator and denominator i.e.
We can see that factorial of a number is product of all integers starting from 1 to that number so we can expand the given values in our question like this
Now we put these values in the given equation (1) to see how we can proceed
Now we see that that both in denominators we have the expansion of
Now we can cancel the terms like this
So we have simplified the fraction in this form.
Additional information: We can check our answer by putting a value of
Let
And now putting the same value in the RHS
So we have obtained the same answer by putting the value of ‘n’.
Note: Knowing properties of factorials helps us in this problem. Factorials can be represented in two ways by putting an exclamation mark (!) after an expression or by putting the number in an ‘L’ shaped symbol. Both the notations are correct and acceptable by the math fraternity.
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