{C₁} + 2{C₂} + 3{C₃} + 4{C₄} + .... + n{Cₙ} =

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7.Binomial Theorem

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${C_1} + 2{C_2} + 3{C_3} + 4{C_4} + .... + n{C_n} = $

A

${2^n}$

B

$n.\,\,{2^n}$

C

$n.\,\,{2^{n - 1}}$

D

$n.\,\,{2^{n + 1}}$

Solution

(c) Trick : Put $n = 1,\,\,2,\,\,3,….$

${S_1} = 1,\,\,{S_2} = 2 + 2 = 4$

Now by alternate $(c)$, put $n = 1,\,\,2$

${S_1} = {1.2^0} = 1,{S_2} = {2.2^1} = 4$

Standard 11

Mathematics

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