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" 5) "quad C(0)-C(2)+C(4)-C(6)+...=...

" 5) "quad C_(0)-C_(2)+C_(4)-C_(6)+...=

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Find the sum C_(0)-C_(2)+C_(4)-C_(6)+........ Where C_(r)=nC_(r)

Find the sum C_(0)-C_(2)+C_(4)-C_(6)+..., where C_(r)=^(6)C_(r)=^(n)C_(r)

Find the sum C_(0)-C_(2) +C_(4)-C_(6)+…. , where C_(r)=^(n)C_(r)

If (1 + x)^(n) = C_(0) + C_(1)x + C_(2)x^(2) + C_(3) x^(3) + C_(4) x^(4) + ..., find the values of (i) C_(0) - C_(2) + C_(4) - C_(6) + … (ii) C_(1) - C_(3) + C_(5) - C_(7) + … (iii) C_(0) + C_(3) + C_(6) + …

If (1+x)^(n) = C_(0) + C_(1)x + C_(2)x^(2) + "….." + C_(n)x^(n) , then find the value of C_(0)+C_(2)+C_(4)+C_(6)+........ ​ ​

If (1 + x)^(n) = C_(0) + C_(1)x + C_(2)x^(2) + C_(3) x^(3) + C_(4) x^(4) + ..., find the values of (i) C_(0) - C_(2) + C_(4) - C_(0) + … (ii) C_(1) - C_(3) + C_(5) - C_(7) + … (iii) C_(0) + C_(3) + C_(6) + …

If (1 + x)^(n) = C_(0) + C_(1)x + C_(2)x^(2) + C_(3) x^(3) + C_(4) x^(4) + ..., find the values of (i) C_(0) - C_(2) + C_(4) - C_(0) + … (ii) C_(1) - C_(3) + C_(5) - C_(7) + … (iii) C_(0) + C_(3) + C_(6) + …

If C_(0), C_(2), C_(4).. . are the binomial coefficients in the expansion of (1+x)^(9) then C_(0)+C_(2)+C_(4)+C_(6)+C_(8) =

" 0.Show that "C_(0)-4.C_(1)+7.C_(2)-10.C_(3)+.....=0

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