The intercepts represent the points where the graph touches the axis the given. With that said, your y intercept is (0, -3) and the x intercept is (-1,0).

6 0

3 years ago

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Does the following infinite series converge or diverge? 1/3+2/9+4/27+8/81+...

PilotLPTM [1.2K]

Note that A and D are ludicrous choices, so you can throw them away outright. (Any divergent series cannot have a sum, and any convergent series must have a sum.)

The sum is certainly convergent because it can be written as a geometric sum with common ratio between terms that is less than 1 in absolute value.

$S=\dfrac13+\dfrac29+\dfrac4{27}+\dfrac8{81}+\cdots$
$S=\dfrac13\left(1+\dfrac23+\dfrac{2^2}{3^2}+\dfrac{2^3}{3^3}+\cdots\right)$

We can then find the exact value of the sum:

$\dfrac23S=\dfrac13\left(\dfrac23+\dfrac{2^2}{3^2}+\dfrac{2^3}{3^3}+\dfrac{2^4}{3^4}+\cdots\right)$

$\impliesS-\dfrac23S=\dfrac13$
$\implies\dfrac13S=\dfrac13$
$\implies S=1$

So the answer is B.

8 0

3 years ago