An Inequality [S]

Prove that
[1/2][3/4]......[9999/10000]< 1/100
[S] See comment for solution.I have solved using the technique that is called 'telescoping'.

A simple inequality[S]

For real nums a,b,c prove that
(i) (a+b)(1/a +1/b)>=4

(ii)(a+b+c)(1/a +1/b +1/c) >=9

(iii) well, if this seems trivial prove in general for reals nums a_1,a_2,...a_n prove that
(a_1 +a_2 +...+a_n) (1/ a_1 +1/ a_2 +...+1/ a_n)>=n^2

(iv) well you may still go further proving (1+1/2 +1/3 +....) is not convergent.[S]