WBJEE · Maths · Binomial Theorem
If \(\mathrm{c}_0, \mathrm{c}_1, \mathrm{c}_2, \ldots \ldots \ldots \ldots \ldots . \mathrm{c}_{\mathrm{n}}\) denote the co-efficients in the expansion of \((1+\mathrm{x})^{\mathrm{n}}\) then the value of \(\mathrm{c}_1+2 \mathrm{c}_2+3 \mathrm{c}_3+\ldots . .+\mathrm{nc}_{\mathrm{n}}\) is
- A \(\mathrm{n} \cdot 2^{\mathrm{n}-1}\)
- B \((\mathrm{n}+1) 2^{\mathrm{n}-1}\)
- C \((n+1) 2^n\)
- D \((n+2) 2^{n-1}\)
Answer & Solution
Correct Answer
(A) \(\mathrm{n} \cdot 2^{\mathrm{n}-1}\)
Step-by-step Solution
Detailed explanation
Hints : \((1+\mathrm{x})^{\mathrm{n}}=\dot{c}_0+\mathrm{xc}_1+\mathrm{x}^2 \mathrm{c}_2+\ldots \ldots . \mathrm{x}^{\mathrm{n}} \mathrm{c}_{\mathrm{n}}\) \(n(1+x)^{n-1}=c_1+2 x c_2+\ldots \ldots . . n x^{n-1} c_n\) Put \(x=1\)…
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