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If $(1 + x) (1 + x + x^{2}) (1 + x + x^{2} + x^{3}) \dots (1 + x$ $+ x^{2} + \dots + x^{n}) = a_{0} + a_{1} x + a_{2} x^{2} + \dots + a_{m} x^{m}$ then the value of $a_{1}$ is

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detailed solution

Correct option is C

a1= coefficient of x in (1+x)1+x+x21+x+x2+x3…1+x+x2+…+xn= coefficient of x in (1+x)n=nC1=n

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If (1+x)1+x+x21+x+x2+x3…(1+x+x2+…+xn=a0+a1x+a2x2+…+amxm then the value of a1 is

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Ready to Test Your Skills?

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If $(1 + x) (1 + x + x^{2}) (1 + x + x^{2} + x^{3}) \dots (1 + x$ $+ x^{2} + \dots + x^{n}) = a_{0} + a_{1} x + a_{2} x^{2} + \dots + a_{m} x^{m}$ then the value of $a_{1}$ is