Question

prove that 2*6*10*14....upto n factors = (2n)!/n! = (n+1)(n+2)....to n factors
(from chapter: permutation and combination) Irrelevant answer will be reported ,
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Answer 1

Answer:

Step-by-step explanation:

2* 6* 10* 14* ..........................*(4n-2)

= (2*1) *(2*3) *(2*5) *................*(2*(2n-1))

= $2^{n}$ *(1*3*5*7*...............................*(2n-1))

= $2^{n}$ *$\frac{1*2*3*4*5*6*.....................*(2n-1)*2n}{2*4*6*8*.............................*2n}$

= $2^n$ * $\frac{1*2*3*4*5*6*.....................*(2n-1)*2n}{2^n(1*2*3*4*5*6*.............................(n-1)*n)}$

=$\frac{1*2*3*4*5*6*.....................*(2n-1)*2n}{(1*2*3*4*5*6*.............................(n-1)*n)}$

=$\frac{2n!}{n!}$                   (proved no. 1)

= $\frac{1*2*3*4*5*6*.....................*(2n-1)*2n}{(1*2*3*4*5*6*.............................(n-1)*n)}$

=$\frac{1*2*3*4*5*6*.........(n-1)*n*(n+1)*(n+2)............*(2n-1)*2n}{(1*2*3*4*5*6*.............................(n-1)*n)}$

=(n+1)*(n+2)...............................(2n-1)2n