Question

If the sum of the coefficients in the expansion of (x+y)n is 4096, then the greatest coefficient in the expansion is ?

Answer 1

Final Answer :924

For Calculation see pic

Answer 2

Given :

Sum of coefficient in expansion of $( x+y )^{n}$ = 4096

To find :

Value of greatest coefficient in the expansion .

Solution :

Sum of coefficient in expansion of $( x+y )^{n}$ = 4096

putting,  x = y = 1 ,

=> $2^{n}$ = 4096 = $2^{12}$

=> n = 12

When n is even , Greatest coefficient in the expansion is  $^{n}C_{n/2}$ .

=> $^{12}C_{6}$

=> ( 12! ) / ( 6! * 6! )

=> 924

Value of greatest coefficient in the expansion  $( x+y )^{n}$  is 924 when the sum of the coefficients in the expansion is 4096 .