Attempt

Mathematics

1 answer:

Pachacha [2.7K]3 years ago

4 0

Answer:

Yes, the triangles are similar by SAS

Step-by-step explanation:

Looking at the picture, we see that there are two triangles with side lengths of different sides. We can deduce that the scale factor is 1 2/3, because 8 divided by 4.8 is 1 2/3, and 10 divided by 6 is the same. Now that we have clarified that the triangles share the same scale factor, we notice that the angle is also the same, as mentioned in the picture. This leads us to say that the triangles are similar by the SAS similarity theorem (Side, Angle, Side). I hope this helped and please don't hesitate to reach out with more questions!

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Let $S_k=\displaystyle\sum_{n=1}^k\frac3{(-2)^n}$ . Then $S_k$ is the $k$ th partial sum.

$S_1$ happens to be the first term in the series, which is why that box is marked correct:

$S_1=\displaystyle\sum_{n=1}^1\frac3{(-2)^n}=\frac3{(-2)^1}=-1.5$

But the next partial sum is not correct:

$S_2=\displaystyle\sum_{n=1}^2\frac3{(-2)^n}=\frac3{(-2)^1}+\frac3{(-2)^2}=-0.75$

and this is not the same notion as the second term (which indeed is 0.75) in the series.

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