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Prove that: .^(47)C(4) + .^(51)C(3) +^(5...

Prove that: `.^(47)C_(4) + .^(51)C_(3) +^(50)C_(3)+^(49) C_(3) +^(48)C_(3) +^(47)C_(3) =^(52)C_(4)`

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`L.H.S = .^(47)C_(4) +^(51)C_(3) +^(50)C_(3)+^(49)C_(3) +^(48)C_(3)+^(47)C_(3)`
`= (.^(47)C_(4)+^(47)C_(3))+^(48)C_(3)+^(49)C_(3)+^(50)C_(3)+^(51)C_(3)`
`= .^(48)C_(4) +^(48)C_(3)+^(49)C_(3)+^(50)C_(3)+^(51)C_(3) ( :' .^(n)C_(r) +^(n)C_(r-1)=^(n-1)C_(r))`
`= .^(49)C_(4) +^(49)C_(3)+^(50)C_(3)+^(51)C_(3)`
`= .^(50)C_(4)+^(50)C_(3)+^(51)C_(3)`
`= .^(51)C_(4)+^(51)C_(3)`
`= .^(51)C_(4) = R.H.S`. Hence Proved.
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