The squares here are organized in a way where one can prove the Pythagorean theorem. The Pythagorean theorem is the theorem that states that the length of one side of a right triangle, squared, plus the length of another leg of the triangle, squared, is equal to the hypotenuse squared. This is a² + b² = c². Since the areas of the squares are the squared lengths of the sides, that means that D. is the right answer.
Answer:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
The objective is to state why the value of
converging alternating seies with terms that are non increasing in magnitude
lie between any two consecutive terms of partial sums.
Let alternating series
<span>Sn = partial sum of the series up to n terms</span>
{S2k} = sequence of partial sum of even terms
{S2k+1} = sequence of partial sum of odd terms
As the magnitude of the terms in the
alternating series are non-increasing in magnitude, sequence {S2k} is bounded
above by S1 and sequence {S2k+1} is bounded by S2. So, l lies between S1 and
S2.
In the similar war, if first two terms of the
series are deleted, then l lies in between S3 and S4 and so on.
Hence, the value of converging alternating
series with terms that are non-increasing in magnitude lies between any two
consecutive terms of partial sums. So, the remainder Rn = S – Sn alternating
sign
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