assignment

1.1 Prove that the square of an even integer is also an even integer. [57 1.2 State any one property of real numbers. [1] 1.3 Solve the inequality and represent your solution on a line graph and in intervals or union of Intervals, (a) 2x + 1 [5] 1.4 Prove by Mathematical Induction that 2" > " for all positive integers n . [5] 1.5(a) State and Prove the Binomial Theorem. (b) In a binomial expansion of (i) ~ + bx 12 [10] , find the coefficient of x -10 [3] (1i) 2x? _ 1 10 3 x 7 , find the 6th term. [3] 1.6 State without proof the Binomial Series. Hence find the series expansion of 1 /1 + x For which values of x is the expansion valid? [5] Use this expansion to estimate 1 1. 1 correct to three decimal places. Compare it with the calculator value. [5]