Specify if the infinite series converges or diverges and show solution \sum _{n=1}^{\infty }\:\frac{n!+6}{n!-2}

Q: Suppose that $\sum_{n=1}^{\infty} a_{n}\left(a_{n} \neq 0\right)$ is known to be a convergent…

A: Given: ∑n=1∞an is convergent. an≠0 To prove: ∑n=1∞1an is divergent.

Q: Use a graph of $y-1 / x$ to show that if $s_{n}$ is the $n$ th partial sum of the harmonic series,…

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Q: Let P be the statement “You get perfect scores in your major exams,” Q be the statement “You do…

A: Now, we have statements P: You get perfect scores in your major exams Q: You do every exercise in…

Q: 7. (4Dª – 4D³ – 23D2 + 12D + 36)y =0 8. (18D3 – 33D² + 20D – 4)y = 0

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Q: f the $n$ th partial sum of a series $\sum_{n=1}^{\infty} a_{n}$ is $s_{n}=3-n 2^{-n}$ ind $a_{n}$…

A: The nth partial sum of the series ∑n=1∞an is Sn=3-n2-n. We have to find an and ∑n=1∞an.

Q: Test the convergence of the series $\sum_{n=1}^{\infty}\left(\frac{2 n+3}{3 n+2}\right)^{n}$

A: Given: ∑n=1∞2n+33n+2n Perform a test of the convergence of the series.

Q: The given power series : 42n (z+6)" is convergent if |( + 6)| < (Write your answer up to 5 digits…

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Q: Suppose that a series $\sum a_{n}$ has positive terms and its partial sums $s_{n}$ satisfy the…

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Q: SOLVE THE FOLLOWING NON-HOMOGENOUS LINEAR DIFFERENTIAL EQUATIONS. y” + y = secx tanx

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Q: \sum_{n=1}^{2} \frac{1}{\sqrt{n+4}}

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Q: If $\Sigma a_{n}$ is a convergent series with positive terms, is it true that $\Sigma \sin…

A: Given: ∑an is a convergent series with positive terms. To check whether ∑sinan is convergent or not.

Q: Find the sum of the series $\Sigma_{n=1}^{\infty} 1 / n^{5}$ correct to three decimal phoces.

A: Given: Find the sum of the series up to three decimal places.

Q: Which of the following infinite series converge? n(n +2) i) =1 (n +3)3 sin (ln n) =1 n(n+3) * Inn…

A: Zindagi

Q: For what values of $p$ is the series $\sum_{n=1}^{\infty} \frac{1}{n^{p}}$ convergent?

A: The given series is: ∑n=1∞1np To find: The values of p such that the given series is convergent.

Q: An important example of an infinite series is the geometric series a+a r+a r^{2}+a r^{3}+\dots+a…

A: A geometric series is a type of infinite series in which each term is obtained by multiplying the…

Q: Determine whether the sequence with the given n^{th} term is monotonic. a_n = {cos n} / n

A: Result:   A given sequence {an} is said to be  monotonic sequence if the given sequence satisfies…

Q: Prove the alternating series $\sum_{n=1}^\infty \frac{(-1)^n}{\sqrt{n}}$ converges without using the…

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Q: Evaluate e^-6 with the two forms of series expansion shown, compare them to the true value of…

A: What is Error: Error is the difference between a genuine value and an estimate, or approximate,…