practice problems pending
Q1. S1. Cross multiply and simplify to get: 9 (10^3013 - 10^2013) > 0 H.P. Q2. S2. Consider only 'a' side. Call it A. 1/A = 1 + a^n/(1 + a + .. a^(n-1)) = 1 + 1/[1/a + 1/a^2 ... 1/a^(n)] Assume 1/A > 1/B We will figure out whether it's true. => 1/[1/a + .. 1/a^n] > 1/[1/b + .. 1/b^n] => [1/b + .. 1/b^n] > [1/a + .. 1/a^n] This is clearly true since a > b. So the original assumption was correct. => 1/A > 1/B => A < B. Q3. a,b,c are real numbers s.t. a >= b >= c. Prove or disprove: a^2 + ac + c^2 >= 3b(a-b+c) S3. Make it a quadratic in b by moving RHS to LHS. And then show D <= 0 So it will be always >= 0 So it will be proved(not disproved).