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balandron [24]
3 years ago
8

In 2-3 sentences describe why the only way an infinite geometric series has a sum is if |r| < 1.

Mathematics
1 answer:
Lina20 [59]3 years ago
4 0
The formula for the sum of geometric series = a (1 - r^n) / 1 - r
when it will be an infinite geometric series. the term r^n will equal to zero because and number < 1 that is raise to the power infinity the answer is zero that is why in a infinite geometric series, sum = a / 1 - r.
if the r < 1 then there will be no numerical answer because the sum will be infinity. that is why r < 1 to have a sum 
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Thus, there are two similar triangles, one with the 10 cm bottom and 15 cm bottom, where one triangle is larger by a factor of 15/10 = 3/2

We know that the 8 cm line segment and y both join to create the side of the large triangle.

8cm + y = the side of the large triangle

Multiplying 8cm by 3/2 gives us 12, since we know the large triangle is 3/2 times larger than the smaller one.

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Finding x is going to be a bit different. We know that the 6 cm line and x form the side of the larger triangle, which we know is 3/2 times larger than x.

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Multiply both sides by 2

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---------------------------------------------------------------------------------------

(b) The following functions are positive in quadrant III:

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The following functions are negative in quadrant III

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