factorials problem

[maxer123]

Does anyone know how to deal with this?:

I know it simplifies to (n+1)(n+2)(n+3)...(2n)=30240 but cant seem to figure out what to do next

 

[Deleted member 4993]

Does anyone know how to deal with this?: View attachment 32000

I know it simplifies to (n+1)(n+2)(n+3)...(2n)=30240 but cant seem to figure out what to do next

Factor out 30240.

30240 = 5 * 6 *1008 = 5 * 6 * 7 *144 ....... continue

It is "brute-force" method but I find it most convenient for this problem.

 

[Steven G]

Trial and error comes to mind.

Solve nⁿ=30240 to get a starting point to start guessing.

 

[Steven G]

Factor out 30240.

30240 = 5 * 6 *1008 = 5 * 6 * 7 *144 ....... continue

It is "brute-force" method but I find it most convenient for this problem.

SK, may I please have one more hint using your method?

 

[BigBeachBanana]

SK, may I please have one more hint using your method?

Continuing SK's method notice you need to multiply two of the factors to fit the pattern (n+1)(n+2)...(2n). From there you can conclude what n is.

 

[Steven G]

Continuing SK's method notice you need to multiply two of the factors to fit the pattern (n+1)(n+2)...(2n). From there you can conclude what n is.

I still don't see it.?

 

[Dr.Peterson]

I still don't see it.?

I think we're just trying to arrange the factors of 30,240 as a product of consecutive whole numbers. It doesn't take long this way.

Of course, you could also just try small values of n, since it can't be too large.

 

[Deleted member 4993]

I still don't see it.?

The intention of my post is to entice the OP to investigate and ask questions - including finding problems with original post.