數學歸納法超急!!!!!!!!!?

1.let P(n):1-1/2+1/3-1/4+...+1/(2n-1)-1/2n
=1/(n+1)+1/(n+2)+1/(n+3)+...+1/2n
Prove that
2.(a)let P(n):1x1+3x4+5x7+...+(2n-1)(3n-2)
=n(4n^2-n-1)/2
Prove that
(b)(I)solve the equation(2x-1)(3x-2)=3290
(ii)find the value of 1x1+3x4+5x7+...+3290
(c)find the value of 15x22+17x25+19x28+...+3290
3.(a)prove 1x3+2x15+3x35+...+n(4n^2-1)
=[n(n+1)(2n^2+2n-1)]/2
(b)using result of (a) and fact that 1+2+3+...+n=n(n+1)/2
Prove 1^3+2^3+3^3=[n^2(n+1)^2]/2
(c)using (b) result and 1^3+3^3+5^3+...+(2n-1)^3
=n^2(2n^2-1)
Express (1^3-2^3)+(3^3-4^3)+...+[(2n-1)^3-(2n)^3]
in terms of n
(d)prove your result in (d) by mathematical induction