Asked by mel gibbs
Express (5x+2)/(2x-1)(x+1) into partial fractions and hence expand the expression as a series in ascending power of x giving the first 4 terms
Answers
Answered by
Steve
(5x+2)/(2x-1)(x+1)
= 3/(2x-1) + 1/(x+1)
Now, think of geometric series where the infinite sum is
S = a/(1-r)
3/(2x-1) = -3/(1-2x) = -3(1+(2x)+(2x)^2 + (2x)^3)
= -3(1+2x+4x^2+8x^3)
= -3 - 6x - 12x^2 - 24x^3
Similarly for 1/(x+1) so we end up with
-2 - 7x - 11x^2 - 25x^3 - ...
= 3/(2x-1) + 1/(x+1)
Now, think of geometric series where the infinite sum is
S = a/(1-r)
3/(2x-1) = -3/(1-2x) = -3(1+(2x)+(2x)^2 + (2x)^3)
= -3(1+2x+4x^2+8x^3)
= -3 - 6x - 12x^2 - 24x^3
Similarly for 1/(x+1) so we end up with
-2 - 7x - 11x^2 - 25x^3 - ...
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.