Page 23 - 11-Math-8 Mathematical Inductions and Binomial Theorem

81.. MQautahdermataitcicEaql Iunadtuiocntisons and Binomial Theorem eeLLeeaarrnn..PPuunnjjaabb

11

( ) iv) y3 in the expansion of x - y

7. Find the coefficient of;

i) x5 in the expansion of  x 2 - 3 10
 2x 

ii) xn in the expansion of  x2 - 1 2n
 x 

8. Find 6th term in the expansion of  x2 - 3 10
 2x 

9. Find the term independent of x in the following expansions.

i)  x - 2 10 ii)  x + 1 10 iii) (1 + x2 )3 1 + 1 4
x   2x2  x2 

10. Determine the middle term in the following expansions:

i)  1 - x2 12 ii)  3 x - 1 11 iii)  2x - 1 2m+1
 x 2   2 3x   2x 


11. Find (2n +1) th term from the end in the expansion of  x - 1 3n
 2x 

12. Show that the middle term of (1 + x)2n is =1.3.5....(2n -1) 2n xn
n!

13. Show that: n  +  n  +  n  + .... +  n n  =2n-1
1   3   5   - 1
     

14. Show that:  n  + 1 n  + 1  n  + 1  n  + .... + n 1  n  =2n+1 - 1
 0  2 1  3  2  4  3  + 1 n  n +1
       

version: 1.1

23