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If (1 + x)^(n) = C(0) = C(1) x + C(2) x^...

If `(1 + x)^(n) = C_(0) = C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n)` , find the values of the following `sumsum_(0 le i lt j le n)C_(i)`

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`underset(0leilt j le n)(sumsum)C_(i)= ((sum_(i=0)^(n) underset(j=0)overset(n)sum) C_(i)-underset(i= j)(sumsum)C_(i))/(2)`
` = ((n+1)sum_(i=0)^(n) C_(i) sum_(i=0)^(n)C_(i))/(2) = n.2^(n-1)`
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ARIHANT MATHS-BIONOMIAL THEOREM-Exercise (Questions Asked In Previous 13 Years Exam)
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  14. In the expansion of ((x+1)/(x^(2/3)-x^(1/3)+1)-(x-1)/(x-x^(1/2)))^10 ...

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  17. Coefficient of x^(11) in the expansion of (1+x^2)(1+x^3)^7(1+x^4)^(12)...

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  18. The sum of coefficients in integral powers of x in the binominal expan...

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  19. The coefficient of x^9 in the expansion of (1+x)(16 x^2)(1+x^3)(1+x^(1...

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  20. If the number of terms in the expansion of (1-2/x+4/(x^2))^n , x!=0, i...

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