# Inequalities, solving problems

1.)

2!·4!·...·20!

1!·3!·...·19! (this is a fraction)

I need to solve this in a closed form. the question is that we need to find out if it is better to solve in its original form or we need to 'help it a little'? Now I typed down the whole exercise.

The other problem:

2./a)

1+ 1/2 + 1/3 +...+ 1/n >10 We need positive n that works for this.

2./b)

We need the smallest n. (not only the answer, we need to prove why that's the answer)

I wrote down all the questions for the exercises. The whole thing is in a sage document. We can upload only sage files to the server too. The teacher is tricky by the way. The subject is called Solving mathematics problems with sage. Sadly I cannot upload pictures because I'd need more karma.

I can try to do this in the analytical way, and type it in sage, but any help or tips would be great with the proof too.. :) I have no idea what my teacher wants really.

This doesn't seem to be a Sage question. There are various math Q&A sites on the internet - though many of them will, rightly, only offer gentle hints to homework.

I don't see how this has anything to do with Sage. You can type in things like `factorial(2)*factorial(4)*factorial(6)` in Sage, or even `prod([factorial(2*i) for i in [1..10]])`, but when someone says "closed form", that sounds like they want something more than just a number. Similarly with the harmonic series thing - you can use Sage to experiment, but it sounds like your teacher wants an *analytic* solution, with a proof. If you can be a little more specific about the Sage part of these questions, that would be helpful.