Question

prove 2.6.10.14.....to n factors = (2 n)!/n! =(n+1)(n+2).....to n factors

Answer 1

solution:

2.6.10.14 ......n

a= 1

n= n

d= 2

An= a+(n-1)d

    = 1+(n-1)2

     = 2n -1

    = 2n (1 . 3 . 5 . 7 ………. 2n-1)

    = 2n ( 1.2.3.4.5.6……2n)/2.4.6.8….2n

   =   2n (2n!)/ 2n(1.2.3…..n)

   =2n/2n (2n!/n!)

  = (2n!/n!)

  = 2nPn

  = (2n!/n!)

  = (n+1) (n+2) ……..(n+n)

Answer 2

hope it helps u ...............