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(C0)/1+(C2)/3+(C4)/5+(C6)/7+.....=...

`(C_0)/1+(C_2)/3+(C_4)/5+(C_6)/7+.....=`

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Prove that (^n C_0)/1+(^n C_2)/3+(^n C_4)/5+(^n C_6)/7+.....+dot=(2^n)/(n+1)dot

Prove that (.^n C_0)/1+(.^n C_2)/3+(.^n C_4)/5+(.^n C_6)/7+ . . . =(2^n)/(n+1)dot

Prove that (.^n C_0)/1+(.^n C_2)/3+(.^n C_4)/5+(.^n C_6)/7+ . . . =(2^n)/(n+1)dot

(8_(C_(0)))/(1)+(8_(C_(2)))/(3)+8_(C_(4))/5+(8_(C_(6)))/(7)+(8_(C_(8)))/(9) =

(C_(0)-C_(2)+C_(4)-C_(6)......)^(2)+(C_(1)-C_(3)+C_(5)-C_(7).........)^(2)=2^(n)

If (1+x)^n =C_0+C_1 x+ C_2 x^2 +....... C_nx^n prove the following : C_0+1/3 C_2+1/5C_4+1/7C_6+.......... = 2^n/(n+1) .

Prove that (.^(n)C_(0))/(1)+(.^(n)C_(2))/(3)+(.^(n)C_(4))/(5)+(.^(n)C_(6))/(7)+"....."+= (2^(n))/(n+1)

Prove that (.^(n)C_(0))/(1)+(.^(n)C_(2))/(3)+(.^(n)C_(4))/(5)+(.^(n)C_(6))/(7)+"....."+= (2^(n))/(n+1)