Give an example of conditionally convergent series n=1 an and n-1 bn such that En=1(an + bn) converges absolutely.

Q: Find an example of two sequences (an)neN and (bn)neN such that both sequences Ei=19 and ₁=1b;…

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Q: Find the sum of the convergent series.

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Q: Determine all values of x where the given power series (a) absolutely convergent and (b)…

A: This series is  ∑n=2∞x+963n136n1n×lnn)    This series will converge only when the numerator is less…

Q: Determine whether the alternating series £ (-1)n+1, n3 converges or diverges. n= 1

A: Given alternating series is  ∑n=1∞-1n+13nn3

Q: Choose the true statements about a convergent series.

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Q: 1 is convergent, and find its sum. Show that the series n(n + 1) n=1

A: we have to show that the given series is convergent and then we have to find the sum. ∑n=1∞1n(n+1)

Q: F(x) = (-1)". n3n n=1

A: Given series ∑n=1∞(-1)nxnn3n

Q: Verify if the resulting series of constant terms when x = 0 is absolutely convergent, conditionally…

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Q: 2. Let {xn} be a sequence of real numbers and yn = Xn-Xn+1 for each n E N. Prove that the series n=1…

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Q: The series

A: We can use ratio test to find the convergence or divergence of the series

Q: Use the Root Test to decide whether 3 п the series EI is convergent or 8n+1) n = divergent.

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Q: Give an example of a conditionally convergent series an such that Σna, con- n=1 n=1 verges.

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Q: 3- (4z-5)" 5"

A: Given: ∑n=0∞4x-5n5n

Q: Show that the series (-1)" (n + 2)² n=1

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Q: - Apply a test to determine whether the series 2 3" converges or diverges. n=1

A: We can use the ratio test here Since L>1 , so this series diverges.

Q: Find the sum of the convergent series n2-3n+2 n=3

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