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Prove that (C0+C1)(C1+C2)(C2+C3)(C3+C...

Prove that `(C_0+C_1)(C_1+C_2)(C_2+C_3)(C_3+C_4)...........(C_(n-1)+C_n)` = `(C_0C_1C_2.....C_(n-1)(n+1)^n)/(n!)`

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We have, `(C_(0)+C_(1))(C_(1)+C_(2))(C_(2)+C_(3))"...."(C_(n-1)+C_(n))`
`=C_(1)C_(2)"...."C_(n-1)C_(n)(1+(C_(0))/(C_(1)))(1+(C_(1))/(C_(2)))(1+(C_(2))/(C_(3)))"....."(1+(C_(n-1))/(C_(n)))`
`=C_(1)C_(2)"...."C_(n-1)C_(n)(1+1/n)(1+2/(n-1))(1+3/(n-2))"...."(1+n/1)`
`=C_(1)C_(2)"....."C_(n-1)C_(n)((n+1)^(n))/(n!)`
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