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Prove that : Prove that 2.C(0)+7.C(1)+12...

Prove that : Prove that `2.C_(0)+7.C_(1)+12.C_(2)+……..+(5n+2)C_(n)=(5n+4)2^(n-1).`

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Prove that : Prove that C_(0)+3.C_(1)+3_(2).C_(2)+……+3^(n).C_(n)=4^(n)

With usual notations prove that 2.C_0 + 7.C_1 + 12.C_2 + ……..+(5n + 2).C_n = (5n + 4).2^(n-1)

With usual notations prove that 2.C_0 + 7.C_1 + 12.C_2 + ……..+(5n + 2).C_n = (5n + 4).2^(n-1)

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Prove that following i) 2.C_(0)+5.C_(1)+8.C_(2)+…..+(3n+2)C_(n)=(3n+4).2^(n-1)

Prove that : C_(0)-3C_(1)+5C_(2)- ………..(-1)^n(2n+1)C_(n)=0

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