Dear Sir - I am in math team at my high and there are question I have that I cannot fiqure how to do from my book or other resources. The questions are as follows:

Simplify: (2log3)(3log4)(4log5)...(31log32)

If 2log(10)= a and 3log(10) = b, find 200log(648) in terms of a and b.

The sum of the first n perfect cubes is 3025. What is the sum of the first n perfect squares?

Find the smallest natural number n such that 1 + 3 to the power of one + 3 to the power of 2 +.... 3 to the power of n > 400.

Solve for x: x/2 + (x/2)squared + (x/2)cubed + .... = 1/x

The expression (x to the power of 8 - 16) can be factored into irreducible quadratic factors. What is the sum of these factors?

Thank so very much! I appreciate it - my teacher doesn't assist me very well!