Decide, whether the following series are convergent or not: eik a) (ik) k=0 k=0 k=1

Q: Q3. For the following power series: En=125 (4x – 16)" i. Find the radius of convergence, ii.…

A: Given power series is ,

Q: divergent? (1+x)-3=1-3x+6x2-10x3........ explain your answer

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Q: Show that the series below is convergent. nn (2п)! n=1

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Q: Determine if the following series converges. Explain your reasoning. sin(k) k2 k=1 8WI

A: Calculating the limit of the series as k tends to infinity.

Q: For which of the following series determine if they are convergent. Illustrate and name the test you…

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Q: 5. Determine whether the following series converges or diverges, and prove your answer: n 2n-j n=1

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Q: Q2. Show that whether the following series converges or diverges n! n=1

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Q: what is the radius high OF convergence of tar nower senes)

A: follow next step

Q: Part IV: Determine whether the following series are convergent or divergent. Use the nth term test…

A: The main objective is to check the convergence or divergence of the series.

Q: Decide, whether the following series are convergent or not: ik? + k 2k+1 a) Σ b) E 2i (2k + 1)!" k=0…

A: Here we use only D'Almbert  ratio test.

Q: For the following power series, determine if convergent. If convergent, find the radius of…

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Q: a. 3y(x²-1)dx + (x³ + 8y − 3x)dy = 0; x = 0, y = 1

A: Given differential equation is  3y(x2-1)dx+(x3+8y-3x)dy=0 ; x=0,y=1 This can be solved by using…

Q: Determine if the following scries converges/diverges: n+ 166 12 – 165 =13

A: We are asked to find the series is convergent or divegent