prove the following by MI

a) 1/(n+1)+1/(n+2)+......+1/(2n)<1
b) The number of pairs of non-negative integers (x,y) satisfying "x+2y=n" is
{ 2(n+1)+[1+(-1)^n] } /4
c) 1+1/sqrt(2)+1/sqrt(3).......+1/sqrt(n)>2[sqrt(n+1)-1]