# Science:Math Exam Resources/Courses/MATH101/April 2017/Question 03 (b)

MATH101 April 2017
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### Question 03 (b)

The interval of convergence of the power series ${\displaystyle \sum _{n=0}^{\infty }nx^{n+1}}$ is ${\displaystyle (-1,1)}$. (You don’t have to show this.) Find a formula (not involving infinite series) for ${\displaystyle \sum _{n=0}^{\infty }nx^{n+1}}$, valid for all ${\displaystyle -1.

 Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!