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For 2<=r<=n,((n),(r))+2((n),(r-1))+((n)...

For `2<=r<=n,((n),(r))+2((n),(r-1))+((n),(r-2))` is equal to

A

`({:(n + 1),(r - 1):})`

B

`2({:(n + 1),(r + 1):})`

C

`2({:(n + 1),(r ):})`

D

`({:(n + 1),(r ):})`

Text Solution

Verified by Experts

`{:((n),(r)):}+2{:((n),(r-1)):}+{:((n),(r-2)):}=[{:((n),(r)):}+{:((n),(r-1)):}]+[{:((n),(r-1)):}+{:((n),(r-2)):}]={:((n+1),(r)):}+{:((n+1),(r-1)):}={:((n+2),(r)):}`
`" "[because""^(n)C_(r)+""^(n)C_(r-1)=""^(n+1)C_(r)]`
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