Step-by-step explanation: They are similar triangles. We know CD and BC. So we can find the comparison between the two. And we see that BC x 7 = CD. So the same will be said for BF and FE. We have BF is equal to 9. So 9 x 7 = 63. However, now we need to add the two together in order to get BE. Because BF + FE = BE. So 9 + 63 = 72

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3 years ago

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mylen [45]

B and C are absurd; if a series converges, it must have a sum, but if a series diverges, it cannot have a sum.

Now, notice that

$\dfrac12+\dfrac29+\dfrac4{27}+\dfrac8{81}+\cdots=\dfrac12+\dfrac{2^{2-1}}{3^2}+\dfrac{2^{3-1}}{3^3}+\dfrac{2^{4-1}}{3^4}+\cdots$

That is, we can write the sum more compactly as

$\dfrac12+\dfrac12\displaystyle\sum_{n=1}^\infty\left(\frac23\right)^n$

The series is geometric with common ratio $\dfrac23$ , so the series converges (and thereby has a sum), so the answer is D.

6 0

3 years ago