The coefficient of the 5th term in the binomial expansion of ((1 + kx)^{8}), in ascending powers of x is (frac{35}{8}). Find the value of the constant k.
-
A.
2 -
B.
(frac{1}{2}) -
C.
(-frac{1}{2}) -
D.
-2
Correct Answer: Option B
Explanation
((1 + kx)^{8} = ^{8}C_{0}(1^{8})(kx)^{0} + ^{8}C_{1}(1^{7})(kx)^{1} + …)
The 5th term = (^{8}C_{5 – 1}(1^{4})(kx)^{4})
= (^{8}C_{4} (kx)^{4})
(implies 70k^{4} = frac{35}{8})
(k^{4} = frac{frac{35}{8}}{70})
(k^{4} = frac{1}{16})
(k = frac{1}{2})