(a) Find the exact value that √n-√n +2 converges to, or else conclude that the series diverges. n=1 1\2

Q: Calculate the third term of the power series of ln (1 + x) if x = 0.5.

A: Calculate the third term of the power series of  if .

Q: 3η2 +1 5. E - 00 =1 6η2-2n+ 3 6 Σ(-1)"+ 1 - + 00 2n n!

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Q: 3n². {(-1y"-1, 4n2 - 1 n-1

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Q: 1. Use the Alternating Series Test to determine whether the series Σ(-1)"+¹ converges absolutely,…

A: Alternating Series Test: A series ∑an where an=-1n+1bn where bn≥0, ∀n is convergent if (i)…

Q: ∞ Σ(-1)^²-¹ (2 −1) en n=1

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Q: Suppose our recursive formula for a power series solution is a2 a3 Find the following in terms of ag…

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Q: 3. Give an example of divergent series n=1dn and Ln=1 6n for which the series ("q + "p) converges.

A: Given: that An example of divergent series ∑n=1∞ an and ∑n=1∞ bn for which the series  ∑n=1∞ an+bn…

Q: n 6n2 m=1 2n²+1,

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Q: Determine whether the series converges absolutely or conditionally, or diverges. 5 (-1)" + '(6n + 8)…

A: The solution are next step..

Q: Σ(-1)*+1 k=1 3k +1 3k4 + k + 6k6

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Q: +∞ Σ x=1 -6 8 3-x 2x

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Q: 5.- Demonstrate that the series converges or diverges. n=1 3n+2

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Q: Determine whether each series converges absolutely, converges conditionally, or diverges 3" E(-1)";…

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Use the Root Test to determine if the series converges or diverges. -104² Σ k=1

A: We need to check the convergence of the series: ∑k=1∞1-10kk2 using the root test.

Q: For each series, determine whether it converges absolutely, converges conditionally, or diverges.…

A: The given problem is to find the given series is convergence or divergence by using series…

Q: 1 5. Determine whether the series S= >) converges or diverges and identify the test you used. (3n +…

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Q: (a) (b) m=0 11=0 (-1)" vn+1 (-1)" √√n+1 元+1 n²-3n+1

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Q: Apply the ratio test to determine whether or not the series converges. (−1)n-13n 2 n² 8 n=1

A: Ratio test is used