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Find the middle term in the expansion of (1+x)^{2n}

  • Option 1)

    2n_{Cn+1}x^{n}

  • Option 2)

    2n_{Cn-1}x^{n}

  • Option 3)

    2n_{Cn}x^{n}

  • Option 4)

    2n+1_{Cn}x^{n}

 

Answers (1)

best_answer

As we learnt in

Middle term in Binomial Expression if n is odd -

If n is odd then

^{n}c_{\frac{n-1}{2}}\cdot x^{\frac{n+1}{2}}\cdot a^{\frac{n-1}{2}} and

^{n}c_{\frac{n+1}{2}}\cdot x^{\frac{n-1}{2}}\cdot a^{\frac{n+1}{2}}

- wherein

Two terms are middle terms and their binomial coefficients are equal.

 

 

 

Middle term in (1+x)^{2n} is ^{}\textrm{2n}C_nx^{n}


Option 1)

2n_{Cn+1}x^{n}

Incorrect option 

Option 2)

2n_{Cn-1}x^{n}

Incorrect option 

Option 3)

2n_{Cn}x^{n}

Correct option 

Option 4)

2n+1_{Cn}x^{n}

Incorrect option 

Posted by

Aadil

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