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## AP®︎/College Calculus BC

### Unit 10: Lesson 15

Representing functions as power series

# Finding function from power series by integrating

AP.CALC:
LIM‑8 (EU)
,
LIM‑8.D (LO)
,
LIM‑8.D.6 (EK)
,
LIM‑8.G (LO)
,
LIM‑8.G.1 (EK)
When a power series S₁ is an antiderivative of a geometric series S₂, we can find the function represented by S₁ by integrating the expression for S₂.

## Want to join the conversation?

• Isn't the answer ln |1-2x| -2?
• No, g'(0)= - 2, but g(0)=0, when we substitute 0 to the second given function. This way c=0 and g(x)=ln |1-2x|
• I would really love to see some context for this massive unit....It's all good to understand how to calculate the interval of convergence for geometric series and power series and their derivatives and integral functions......but what is it good for?
• Why do we substitute x with 0 to find C?
(1 vote)
• We need to find C in order to determine what the function actually is. We know that the equation holds for all x, so we can plug in any x we like to get an equation where we can solve for C. We choose x=0 because it makes almost everything vanish, so solving for C is easier.
• isn't the other function the infinite series -2x/n*(1-2x)?