Question

Find n so that the coefficients of the 11th and 13th terms are the same. (1+x)^n

Answer 1

@jim_thompson5910 @Mertsj

Answer 2

@AriPotta @abb0t

Answer 3

@so1d

Answer 4

whats ur reason oldrin

Answer 5

It follows from the fact that the binomial coefficients, when arranged in a triangle (Pascal's triangle), are symmetric down the middle:Here, we wish for our 11th and 13th coefficients (corresponding to the 11th and 13th numbers in the \(n\)-th row of Pascal's triangle) to be equal; as you can see from the sketch of the triangle, this is satisfied by symmetry, so we merely need to pick the number right in between :-)