If ( 1 + x ) 2 n = a 0 + a 1 x + a 2 x 2 + … . + a 2 n x 2 n then

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Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremProperties of Binomial coefficientsMedium2 minQB

MathematicsMediummultiple choice

If $(1 + x)^{2 n} = a_{0} + a_{1} x + a_{2} x^{2} + \dots . + a_{2 n} x^{2 n}$ then

Options:(select one or more)

Answer:

A, B, C

Solution:

$a_{0} + a_{1} + a_{2} + \dots = 2^{2 n}$ and $a_{0} + a_{2} + a_{4} + \dots = 2^{2 n - 1}$ $a_{n} =^{2 n} C_{n} =$ the greatest coefficient, being the middle coefficient $a_{n - 3} =^{2 n} C_{n - 3} =^{2 n} C_{2 n - (n - 3)} =^{2 n} C_{n + 3} = a_{n + 3}$

Stream:JEESubject:MathematicsTopic:Binomial TheoremSubtopic:Properties of Binomial coefficients

⏱ 2mℹ️ Source: QB

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