Is it true that if E=1a, is a divergent series of positive numbers, then there is also a divergent series E-1b, of positive numbers with b, < a, for every n? Is there a “smallest" divergent series of positive numbers? Give reasons for your answers.

Q: Determine the convergence or divergence of the series.

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Q: Write out the first four terms of the Maclaurin series of f(x) if f(0) = 5, f' (0) = 9, f"(0) = -7,

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Q: Obtain the nth term of the pover series of In(1+x) for the power n= 5 and for a value of x = 0.80

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Q: The sum of the series n-16) is: A) 1. B) 2. C) D) E) Diverges.

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Q: In n 32. n=1 nº ( is defined bu

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Q: Proceed as in Example 3 in Section 6.1 to rewrite the given expression using a single power series…

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Q: 1 The first four nonzero terms of the series of V1+ x

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Q: (2) Prove by induction the standard formula for the sum of the first n + 1 terms of a geometric…

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Q: any method to determine if the series converges or diverges. Give reasons for (n!)8 Σ (7n)! = 1

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Q: Find the first five terms of a power series for e*. +4

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Q: 12. Find the interval and radius of convergence of the series k=1

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Q: an Suppose 2 a, and 2 bn are series with positive terms. If lim = c, where c is and value of C is…

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Q: Find the sum of the following series using Taylor Series. E(-1)" п! n=0

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Q: b. Find the interval and radius of convergence of the given series 27 (х — 3)" n2 n=1

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Q: 2. Suppose E a, and E b, are series with positive terms and 2 b, is known to be divergent. (a) If a,…

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Q: Consider the following series. Vn + 5 n2 n = 1 On your paper, re-right the series of the sum of two…

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Q: In(1 – x) 4. Expand the function y=- in the power series by the powers of x, indicate the interval…

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Q: Use the first three non-zero terms of the Maclaurin series of 1 to calculate (1-t)³ -3 3

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Q: Determine convergence or divergence of the alternating series. 00 6n + 3 E(- 1)" In 6n + 2 n= 1 O…

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Q: If E an is a convergent series with positive terms, is it true that the series ( a) Σ(1+ α) (b)…

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Q: Consider the series 2n Σ n=0 3n +1 by the test of divergence, O lim a, #0 , so the series diverges n…

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Q: Write the Maclaurin's series up to 5 terms of the function 1- 8x

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Q: What is the coefficient of x* in the power series obtained in Question 3(f)?

A: Maclaurin series is a power series.

Q: 4. Find the x3 term of the power series X for the product of these power series Ex4 (A + Bx + Cx² +…

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Q: Σ 00 1 en Diverges n=1

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Q: Suppose Ea, and Eb, are series with positive terms and Eb, is known to be divergent. If a, > b, for…

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Q: 4. Show that if E a, and E* b, are two divergent series of positive terms, E (an + b„) is divergent.

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Q: Find the radius of convergence of the power series. 00 E(-1)"n+ 9 n = 0

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