Question
The value of the term middle in the expansion (2x2 + 1)10 , x=0.5 is:
(a) 77
(b) 462
(c) 330
(d) 252
what is the answer and how ?
(a) 77
(b) 462
(c) 330
(d) 252
what is the answer and how ?
Answers
Steve
you have (2x^2+1)^10
the middle term in the 10th row of Pascal
's triangle has C(10,5) for its coefficient.
That term is C(10,5) (2x^2)^5 1^5 = 252 * 32 x^10
.5^10 = 1/2^10 = 1/1024
252*32/1024 = 63/8
Hmm. Apparently you just have (2x+1)^10, so the middle term is 252*32/32 = 252
the middle term in the 10th row of Pascal
's triangle has C(10,5) for its coefficient.
That term is C(10,5) (2x^2)^5 1^5 = 252 * 32 x^10
.5^10 = 1/2^10 = 1/1024
252*32/1024 = 63/8
Hmm. Apparently you just have (2x+1)^10, so the middle term is 252*32/32 = 252