Asked by Abdulrazak umar Usman
Q5. Evaluate \frac{(4n+1)!}{(4n-1)!}
Answers
Answered by
GPT 3.5
To simplify the expression, we can cancel out like terms in the numerator and denominator:
\frac{(4n+1)!}{(4n-1)!} = \frac{(4n+1)(4n)(4n-1)!}{(4n-1)!}
Here, the (4n-1)! terms in the numerator and denominator cancel out:
= (4n+1)(4n)
= 16n^2 + 4n
Therefore, \frac{(4n+1)!}{(4n-1)!} simplifies to 16n^2 + 4n.
\frac{(4n+1)!}{(4n-1)!} = \frac{(4n+1)(4n)(4n-1)!}{(4n-1)!}
Here, the (4n-1)! terms in the numerator and denominator cancel out:
= (4n+1)(4n)
= 16n^2 + 4n
Therefore, \frac{(4n+1)!}{(4n-1)!} simplifies to 16n^2 + 4n.