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Effectus [21]
3 years ago
7

Find a power series representation for the following function.

Mathematics
1 answer:
PSYCHO15rus [73]3 years ago
5 0

a. Recall that

For , we have

By integrating both sides, we get

If , then

so that

We can shift the index to simplify the sum slightly.

b. The power series for  can be obtained simply by multiplying both sides of the series above by .

c. We have

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Answer: A. Use Pythagorean Theorem to prove that KL is equal to c.

=========================================================

Explanation:

If we could show that KL = c, then we can tie together the following pairs of segments

  • EG = KM = a
  • GF = ML = b
  • EF = KL = c

Then we'd use the SSS congruence theorem to prove the triangles are congruent. The last step is to use CPCTC to conclude that angle EGF is a 90 degree angle.

Keep in mind that we need to know the actual numeric values of 'a' and 'b' to be able to determine the value for c. So without the numbers, the Pythagorean theorem isn't really useful; however, I can see where your teacher is going with this line of logic. Your teacher is effectively just laying out a basic outline more or less.

----------

Notes:

  • SSS = side side side
  • CPCTC = corresponding parts of congruent triangles are congruent
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