prove that : 〖C_0〗^2 + 〖C_1〗^2 +〖C_2〗^2+………+〖C_n〗^2 = (2n)!/n!n!

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`(C_0)^2+ 2 (C_1)^2 + 3 (C_2)^2 + 4 (C_3)^2...+(n+1) (c_n)^2` `(C_0)^2+ 2 (C_1)^2 + 3 (C_2)^2 + 4 (C_3)^2...+(n+1) (c_n)^2`
Prove that `(^(2n)C_0)^2+(^(2n)C_1)^2+(^(2n)C_2)^2-+(^(2n)C_(2n))^2-(-1)^n^(2n)C_ndot` Prove that `(^(2n)C_0)^2+(^(2n)C_1)^2+(^(2n)C_2)^2-+(^(2n)C_(2n))^2-(-1)^n^(2n)C_ndot`
Binomial Thm|C_0^2 + C_1^2 + C_2^2 + ... + C_n^2 = (2n)!/n!n! | Diploma M1| Class11| IIT-JEE Binomial Thm|C_0^2 + C_1^2 + C_2^2 + ... + C_n^2 = (2n)!/n!n! | Diploma M1| Class11| IIT-JEE
Prove that : (C_0+C_1)( C_1+C_2)( C_2+C_3)……….( C_(n-1)+C_n) = (C_0.C_1.C_2……C_(n-1) 〖(n+1)〗^n)/n! Prove that : (C_0+C_1)( C_1+C_2)( C_2+C_3)……….( C_(n-1)+C_n) = (C_0.C_1.C_2……C_(n-1) 〖(n+1)〗^n)/n!
Prove that : C_0 + C_1/2 + C_2/3 + …… + C_n/(n+1) = (2^(n+1)-1)/(n+1) Prove that : C_0 + C_1/2 + C_2/3 + …… + C_n/(n+1) = (2^(n+1)-1)/(n+1)
`C_0/(1.2)+C_1/(2.3)+C_2/(3.4)+........C_n/((n+1)(n+ 2))=` `C_0/(1.2)+C_1/(2.3)+C_2/(3.4)+........C_n/((n+1)(n+ 2))=`
Prove that : C_1/C_0 + 〖2C〗_2/C_1 + 〖3C〗_3/C_2 +……+ 〖nC〗_n/C_(n-1) = (n(n+1))/2 Prove that : C_1/C_0 + 〖2C〗_2/C_1 + 〖3C〗_3/C_2 +……+ 〖nC〗_n/C_(n-1) = (n(n+1))/2
Binomial theorem: Additional questions 1: C0^2-2C1^2+3C2^2-4C3^2+..+(-1)^n(n+1)Cn^2=? Binomial theorem: Additional questions 1: C0^2-2C1^2+3C2^2-4C3^2+..+(-1)^n(n+1)Cn^2=?