`C(n,1)=`

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Delta[[ Prove that ,, 11,1,1nC1,(n+1)C1,(n+2)C1(n+1)C2,(n+2)C2,(n+3)C2]]=1

If ^(n)C_(r)+^(n)C_(r+1)=^(n+1)C_(x), thenx =rb .r-1 c.n d.r+1

""^((2n + 1))C_0 - ""^((2n+ 1))C_1 + ""^((2n + 1))C_2 - ……+""^((2n + 1))C_(2n) =

""^((2n + 1))C_0 - ""^((2n+ 1))C_1 + ""^((2n + 1))C_2 - ……+""^((2n + 1))C_(2n) =

|{:(1,1,1),(""^(n)c_1,""^(n+1)c_1,""^(n+2)c_1),(""^(n+1)c_2,""^(n+2)c_2,""^(n+3)c_2):}|=1

""^((2n + 1))C_0 + ""^((2n+ 1))C_1 + ""^((2n + 1))C_2 + ……+""^((2n + 1))C_n =

""^((2n + 1))C_0 + ""^((2n+ 1))C_1 + ""^((2n + 1))C_2 + ……+""^((2n + 1))C_n =

Prove that .^n C_0 .^n C_0-^(n+1)C_1 . ^n C_1+^(n+2)C_2 . ^n C_2- .. =(-1)^n .