Question

The greatest coefficient in the expansion of 1+x whole raise to power 2n+ 1 is​

Answer 1

Dear student,

The given expansion is (1+x)2n+1The greatest coefficient in the expansion of (1+x)n is coefficient of middle terms.      here 2n+1 is odd ∴ the middle terms are (2n+22)th, (2n+42)th  i.e (n+1)th & (n+2)th                      Tn+1=Cn2n+1xn   or     Tn+2 = Cn+12n+1 xn+1The greatest coefficient in the expansion of (1+x)2n+1  are  Cn2n+1, Cn+12n+1The given expansion is 1+x2n+1The greatest coefficient in the expansion of 1+xn is coefficient of middle terms.      here 2n+1 is odd ∴ the middle terms are 2n+22th, 2n+42th  i.e n+1th & n+2th                      Tn+1=Cn2n+1xn   or     Tn+2 = Cn+12n+1 xn+1The greatest coefficient in the expansion of 1+x2n+1  are  Cn2n+1, Cn+12n+1