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Maths IXC

Date of submission- 3/1/2011

Mrs.Sreekumar R, PGT Mathematics

 

Principle of mathematical induction

Prove the following by using principle of mathematical induction-

    1. =-1)/2

    2. 1.2.3 + 2.3.4 + …+ n(n+1)(n+2) =[n(n+1)(n+2)(n+3)]/4.

    3. 1.2 + 2.3 + 3.4 + …+ n(n+1) =[n(n+1)(n+2)]/3.

    4. n(n+1)(n+5) is a multiple of 3.

    5. (2n+7)< .

    Linear inequalities

    Solve the inequalities-

    1.2<3x-4<5

    2.6<-3(2x-4)<12

    3.-3<4(-7x/2)<18

    4.-12<4-(3x/-5)<2

    5.7<(3x+11)/2<11

    Binomial Theorem

    1. Find a, b and n in the expansion of if the first three terms of the expansion are 729,7290,30375, respectively.
    2. Find a if the coefficients of and in the expansion of are equal.
    3. Evaluate .
    4. If a and b are distinct integers, prove that a-b is a factor of – , whenever n is a positive integer.
    5. Find an approximation of .
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