7. Let s, = aı + a2 + .+ an be the nth partial sum of a series > an. The series converges if and only if n=1 (а) lim an — 0. (b) lim sn is a (finite) real number. n00 (c) lim an is a (finite) real number.

Q: Since lim k→+0 (k + 1)!/3k+1 k!/3* k+1 lim k→+∞ 3 +00, k! the series…

A:

Q: Consider the series ak where (k!)² [(2k)!]² ak In this problem you must attempt to use the Ratio…

A: Given that ak=k!2(2k)!2or, L=limk→∞(k+1)!2(2(k+1))!2k!2(2k)!2or,…

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: Find the interval of convergence of the power series 3x" n2 n=1

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Q: 19. Give an example of divergent series E ak and E, bu such that the series E akbk converges.

A:

Q: Suppose that a power series f(x) = L a„x" n=0 has the radius of convergence p > 0 and that L.- anp"…

A:

Q: 3. Give an example of a convergent series Exn and a divergent series Eyn Ssuch that E(xn + yn) is…

A: Let ∑ xn be a convergent series and ∑ yn be a divergent series

Q: 30. Suppose that E-o Cnx" converges when x when x = 6. What can be said about the convergence or…

A: We have the given series is ∑n=0∞cnxn is convergent for x=-4 and divergent when x=6. Let R be the…

Q: Suppose that the nth partial sum of a series (∑∞n=1  an) is sn = (n+1) /( n+2). Is the series…

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Q: п(п + 1) Compute the general term an of the series with the partial sum Sn -, п> 0. an

A:

Q: 2. Find the interval of convergence for the series. n=1 (x - 7) n n5n

A:

Q: 2. Determine and justify whether Σ-υ i=1 is convergent or divergent. If it is convergent, give the…

A:

Q: Find the largest interval (in x) where the series summation from n = 1 to infinite of xe-nx…

A: Here we use D'Almbert ratio test.

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: Suppose that the power series Сn (2а — 3)" n=0 converges when x = 5.5 but not when x = -5.5. If its…

A: see below the answer

Q: 00 If 2 X, is absolutely convergent series with 2X,= Ixl, then 2 xn=x. n=1 n=1 n=1 Select one: O…

A: Given that ∑n=1∞xn is absolutely convergent. And ∑n=1∞xn=x then ∑n=1∞xn=x. A series ∑an is called…

Q: Find the interval of convergence of the series Σ 27n(x-4)3n+2 from n=0 to infinity

A:

Q: (2 2 First find the sum of this Series: (-1)"b)" the valnes of x for which the given series…

A: ∑n=1∞-1n x-1n3n=∑n=1∞-1nx-13n=∑n=1∞13-x3nFirst term (a) =13-x3,  common ratio (d)=13-x3Sum of the…

Q: 2. Express as a single power series form: Ea,(x– 2)" + (n + 1)a,»,(x – 2)** n%3D2

A: we have to form the single power series from the given power series.

Q: 2. Determine if the series 3n 1 n=1 converges or diverges.

A:

Q: If the radius of convergence of the power series > Cn(x– 5)" is 5, then the radius of convergence…

A: Given that: Radius of convergence of the below power series is 5. To find the radius of convergence…

Q: (3x – 4)* is - The radius of convergence of the series 9k k=0

A:

Q: 9. Estimate the value of the convergent series 8 k=1 (-1)^² k! + 2k with an absolute error less than…

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Q: Find the radius of convergence and interval of convergence of the series. 2n=1 2"(n²+1)

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Q: The series > n=1 1 (a) converges because lim = 0. n0 Vn (b) diverges because lim = 0. (c) converges…

A:

Q: I need help determining if the series (-1)k times (1/radical (k-1)) from k=2 to infinity, absolutely…

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Q: Find the interval of convergence of the series. (5х)" 2" n=1

A:

Q: If given 1 1 1 1 +... determine whether the given series convergent or divergent ---+ 3 6 9 12 using…

A: Here we have to use the ratio test for checking the convergence of series

Q: 8.4.12 Determine whether the series is convergent or divergent. Sigma (-1)^k (k+1)/k^3 from k=2 to…

A: Consider the given series

Q: Suppose that the nth term of the sequence of partial sums for a given series is Sn = 1+2n+3n² 4n²…

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Q: Suppose the series a; has a sequence of partial sums given by sn = 1+ n²–1 2n2+3' Determine i=1 if…

A: Given that ∑i=1∞ai has a sequence of partial sum as sn=1+n2-12n2+3. A series converges means its…

Q: If the radius of convergence of the series E Un x" is R then the radius n=1 of convergence of the…

A:

Q: 2. Consider that > (x – 2)* is a geometric series. As such, for what values of x will this infinite…

A: Given that ∑k=0∞x-2kTo find : Value of xSolution :∑k=0∞x-2kRatio test ak=x-2k…

Q: Find the interval of convergence of the series k(x+ 2)* 5k+1 k=1

A: The given series is: ∑k=1∞k(x+2)k5k+1...(1) Let, ak=k(x+2)k5k+1; k≥1

Q: Compute the general term an of the series with the partial sum Sn = 2 n + 2 , п> 0. 2" %3| - An =

A:

Q: Determine whether the alternating series converges. Σ k + 1 7k + 1 k=1

A: ∑k=1∞(-1)k+1k+17k+1  Above Series is an alternating seriesApply Liebnitz Testlet   ak=k+17k+1…

Q: Compute the general term an of the series with the partial sum Sn = √n, n ≥ 1

A: topic- sequence and series

Q: Suppose you are told that the sequence (Sn) of partial sums of a series with positive terms…

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Q: Compute the general term an of the series with the partial sum Sn n(n + 1) -,n > 0. 2 An = If the…

A:

Q: 5. Determine whether the series E -(-1)*52a÷1 converges absolutely, converges conditionally or 25n-2…

A: Explanation of the answer is as follows

Q: 1 – 4x)k Ek=1 k k3

A: In the question we have to find interval of convergence.

Q: Since 3 (k + 1)³/3k+1 (1+ ±)* 1 lim k→+∞ lim k→+∞ 3 3 the series (converges/diverges/inconclusive)…

A:

Q: 2" (г — 8)т Find the interval of convergence of the power series m

A:

Q: 21. Find the sum of the convergent series. n =0

A: ∑n=0∞434n We can simplify, = ∑n=0∞22.2-2n3n = ∑n=0∞22-2n3n =4∑n=0∞2-2n3n  = 4∑n=0∞34n

Q: (-1)"x2 Is The interval of convergence of the power series 22n! Select one: O a. (-00, 00)

A:

Q: Consider the series 00 n E In n + 2 n=1 Determine whether the series converges, and if it converges,…

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Q: Let fn(x) be the following sequence (not series) of functions n2 fn(x) = (x2 + 7x + 6)n² +n

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Q: Let s, = a1 + az+ ·…+a, be the nth partial sum of a series Σ am- The series converges if and only if…

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Q: 1. Determine whether the series ż 1 2n+1 1 2n-1) converges or diverges by examining the

A: Given series is ∑n=1∞12n+1-12n-1

Q: Show that the series n" (2n)! is convergent. Deduce that lim 0. (2n)! n=1

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.