²nCn+1 +2.²Cn+2n Cn-1=
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Step-by-step explanation:
Answer
n!
(2n!)
=2
n
(1.3.5...(2n−1))
RHS =(1.3.5...(2n−1))2
n
Multiply and divide by 2.4.6...2n on RHS
[1.3.5...(2n−1)]2
n
=(1.3.5...(2n−1))2
n
×
2.4.6....2n
2.4.6...2n
=
2.4.6....2n
[1.3.5...(2n−1)]2
n
=
2.4.6....2n
[(2n)(2n−1)....5.4.3.2.1]2
n
=
2.4.6....2n
(2n)!2
n
=
2
n
(1.2.3..n)
(2n)!2
n
=
n!
(2n)!
= LHS .proved
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