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if $(1 + x)^{15} = C_{0} + C_{1} x + C_{2} x^{2} + \dots + C_{15} x^{15}$ then $C_{2} + 2 C_{3} + 3 C_{4} + \dots + 14 C_{15}$ is equal to

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14⋅214

13⋅214+1

13⋅214−1

None of these

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detailed solution

Correct option is B

we have (1+x)15=C0+C1x+C2x2+…+C15x15⇒ (1+x)15−1x=C1+C2x+…+C15x14On differentiating both sides w.r.t. x, we getx⋅15(1+x)14−(1+x)15+1x2=C2+2C3x+…+14C15x13On putting x = t, we get C2+2C3+…+14C15=15⋅214−215+1=13⋅214+1

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if (1+x)15=C0+C1x+C2x2+…+C15x15 then C2+2C3+3C4+…+14C15 is equal to

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if $(1 + x)^{15} = C_{0} + C_{1} x + C_{2} x^{2} + \dots + C_{15} x^{15}$ then $C_{2} + 2 C_{3} + 3 C_{4} + \dots + 14 C_{15}$ is equal to