**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__

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

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