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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
`underset(0leile jlen)(sumsum)(i +j)(C_(i)pmC_(j) )^(2)`

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Verified by Experts

The correct Answer is:
`n^(2) . 2^(n) + {2^(2n-1) - (2n!)/(2(n!)^(2))}`
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ARIHANT MATHS ENGLISH-BIONOMIAL THEOREM-Exercise (Subjective Type Questions)
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  6. C1/C0+2C2/C1+3C3/C2+............+nCn/C(n-1)=(n(n+1))/2

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  12. If (1 + x)^(n) = C(0) = C(1) x + C(2) x^(2) + …+ C(n) x^(n) , find...

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  13. Evaluate sum(0 le i le j le 10) ""^(21)C(i) * ""^(21)C(j).

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  14. Find the coefficient of x^4 in the expansion of (1+x+x^2+x^3)^(11)dot

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  15. Find the coefficient of x^4 in the expansion of (2-x+3x^2)^6dot

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  17. If for z as real or complex such that (1+z^(2) + z^(4))^(8) = C(0)...

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