Question

The coefficients corresponding to k = 0, 1, 2, ..., 6 in the expansion of (x + y)⁶ are ____O A. 1,6, 15, 15, 6, 1OB. 0,6,15, 20, 15, 6, 0O C. 1, 6, 15, 20, 15, 6, 1O D. 0,1, 6, 15, 15, 6, 1,0

Answer 1

Given the expression :

`(x+y)^6`

so, the coefficients will be calculated using the pascal triangle :

when the power is 1 : coefficients are 1 , 1

when the power is 2 : coefficients are 1 , 2 , 1

when the power is 3 : coefficients are 1 , 3 , 3 , 1

when the power is 4 : coefficients are 1 , 4 , 6 , 4 , 1

when the power is 5 : coefficients are 1 , 5 , 10 , 10 , 5 , 1

when the power is 6 : coefficients are 1 , 6 , 15 , 20 , 15 , 6 , 1

so, the answer is option C. 1, 6, 15, 20, 15, 6, 1

see the following image that represents pascal triangle