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Single Variable Calculus

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Moderate

Working with Divergent Series

SVCALC-BETFKM

The series:

$$1-1+1-1+\ldots$$

...is plainly divergent (its terms don't go to 0).

Nevertheless, the series:

$$1r^0-1r^1+1r^2-1r^3+\ldots$$

...converges for $ - 1 < r<1$. Call the sum of the second series $S(r)$.

Compute:

$$\lim_{r\to 1^-} S(r)$$

A

$-1$

B

$-\cfrac{1}{2}$

C

$0$

D

$\frac{1}{2}$

E

$1$