Verify that for all n ≥ 1,
2*6*10*14… (4n-2) = (2n)! /n!
Basic Step:
(4(1)-2) = (2(1)1!/1!
2 = 2
Assume P(k) is true
Show that P(k+1) is true
2*6*10*14… (4n-2)*(4(n+1)-2) = (2n+1)! /(n+1)!
Consider:
2*6*10*14 … (4n-2) * (4n+2) = (2n+1)! /(n+1)!
Okay this is where my confusion comes in, if I am correct up to this point.
I know that on the left side 2*6*10*14 … (4n-2) = (2n)!/n!
So now is my equation : (2n)!/n! *(4n+2) =(2n+1)! /(n+1)!
Ok have I proceeded correctly so far and if not where am I going wrong, what should my next step be.
Any help would be greatly appreciated.