Find the 6 the term in the expansion of  [ 1/x^(8/3) + ( X^2)* (log(x) ]^8 . Please show all the steps to get the full solution.

Asked by sudhanshubhushanroy | 6th Nov, 2017, 08:59: PM

Expert Answer:

left parenthesis r plus 1 right parenthesis t h space t e r m space i n space b i n o m i a l space e x p a n s i o n space i s space g i v e n space b y space
T subscript r plus 1 end subscript equals to the power of n C subscript r open parentheses x close parentheses to the power of n minus r end exponent open parentheses y close parentheses to the power of r
h e r e space n space equals space 8
r plus 1 equals 6 comma space r equals 5
x space i s space open parentheses 1 over x close parentheses to the power of 8 over 3 end exponent
y space i s space open parentheses x squared space log space x close parentheses

s o space
T subscript 6 equals to the power of 8 C subscript 5 open parentheses open parentheses 1 over x close parentheses to the power of 8 over 3 end exponent close parentheses to the power of 8 minus 5 end exponent open parentheses open parentheses x squared space log space x close parentheses close parentheses to the power of 5
s i m p l i f y space f u r t h e r

Answered by Arun | 13th Dec, 2017, 05:30: PM