Question

If n is even and the value of nCr, is maximum, then r=​

Answer 1

If n is even and the value of nCr, is maximum, then r=​ n/2

Step-by-step explanation:

The binomial coefficient series is

ⁿC₀, ⁿC₁, ⁿC₂, …., ⁿCr, …., ⁿCₙ₋₂, ⁿCₙ₋₁, ⁿCₙ

the task is to find maximum value of ⁿCr

The value of coefficients increasing initially and reaches its maximum and then start reducing  value in middle is maximum

total term are = n + 1

ⁿCr  is r + 1 th term

middle term = (n + 1 + 1)/2  = n/2 + 1  

r + 1 = n/2 + 1  

=> r = n/2

If n is even and the value of ⁿCr, is maximum, when r=​ n/2

if n is odd, the maximum occurs at r=(n−1)/2 and at r=(n+1)/2.

r = n/2   if n is Even

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Answer 2

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