Prove that if n > 1, the nth partial sum of the harmonic series is not an integer. Hint: Let 2* be the largest power of 2 that is less than or equal to n and let M be the product of all odd integers that are less than or equal to n. Suppose that s, = m, an integer. Then M2 s, = M2*m. The right side of this equation is even. Prove that the left side is odd by showing that each of its terms is an even integer, except for the last one.

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Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the…

A: To find whether given series converges or not and if yes then find sum.

Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the…

A: Let's find.

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A: on solving this we get

Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the…

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Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the…

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Q: Determine whether the series converges, and if so find its sum. 4k+2 Σ k=1

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A: We have given∑k=0∞(67)k+3

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A: answer is in step 2

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Q: Prove that if n > 1, the nth partial sum of the harmonic series is not an integer. Hint: Let 2* be…

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Q: Determine whether the series converges, and if so find its sum. 4k+2 7k-1 k=1

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Q: Find a formula for the nth partial sum of the series and use it to determine if the series converges…

A: Please see the explanation below

Q: Determine whether the series converges, and if so find its sum. Σ 4k+2 7k-1 k=1

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A: Explanation of the answer is as follows

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A: The given series is: ∑k=0∞56k+3=563+564+565+566+... which is a geometric series with the first term…

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Q: Verify that the infinite series diverges. 00 1) 1000 (1.055)" arit es mus asi n=0

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.