Show that > iP converges to a finite value iff p < –1. i=1

Q: Find the Value of p which intagral the Converges, abso leste ly Cosn du- Conditionaly. to Jean de

A: Comment: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: oblem 3. Use the integral test to determine whether Y converges or diverges.

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

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Q: Use the integral test to determine if the series 1 n5/2 converges or diverges.

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Q: 6. Use e 6 delinition and prove that he soquence, baving general term converges to 3.

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Q: Sn(x) = e-(2-n)a

A: Given that, fnx=e-x-n2 To show that the given function is uniform convergence at [-1,1]. Let,…

Q: Find the interval of convergence : En-0 (x-3)"

A: Apply ratio test to find the interval of convergence. When L&lt;1 then series converges and When…

Q: +o0 (-1)*n" sin" () Σ 2n n=1

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Q: Use the Integral Test to determine whether the seriesconverge or diverge. Be sure to check that the…

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Q: Let {fn(x)} : „x ER and > 0. 1+ nx Show that ift>0, the sequence {fn(x)} converges uniformly on

A: Given: To explain the given statement as follows, To show that if t&gt;0, the sequence fnx converges…

Q: Suppose that dz converges. What can we conclude about the constant p? Op>1 Op Op< 3

A: Explanation of the answer is as follows

Q: (c) Show that fn (x) : x2+n? converges uniformly on [0, 0).

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Q: Use the Integral Test to determine the convergence or divergence of the p-series. n = 1 dx =…

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Q: Use the Limit Comparison Test to determine whether converges or diverges. Vnvn +1 n=1

A: we have to test whether the given series is convergent or divergent by limit comparison test

Q: Σ Show that n2 + 1 converges/diverges n

A: The given series is: ∑n=1∞nn2+1 Let  an=nn2+1,n≥1    =nn21+1n2   =1n1+1n2 And, bn=1n

Q: 10 Show that (S) converges to a continuous function, but not uniformly. Use the series E f, to show…

A: Solution: The function fnx is defined as follows: fnx=0              x&lt;1n+1sin2πx     1n+1≤x≤1n0…

Q: #2. Give a counter exa mple that (Sn) is bounded but not convergent.

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Q: Determine whether the following converges or diverges. 2n + 1

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Q: Suppose that p(x) = >` anx" converges on (-1, 1], find n=0 the interval of convergence of p(7x – 5)…

A: To find the interval of convergence.

Q: 2k と(+ 1) converges. Use the integral test to determine whether k-1

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Q: Vn +1- n –1 n=1

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Q: Use the Integral Test to determine the convergence or divergence of the p-series. Σ 5 n = 1 00 = xp…

A: we use integral test to find out series converges

Q: Does the series from 1 to infinity of 1/(3^k-2^k) converge or diverge using the limit comparison…

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Q: Find the smallest positive integer n so that S, approximates the sum of the convergent ser to four…

A: Here we have to find the smallest positive integer n so so the Sn, approximates the sum of the…

Q: The series 1 k ln k k=2 converges. Choose an option: ()Real ()False

A: Integral Test : Suppose that f(x) is a continuous , positive and decreasing function on the interval…

Q: . Use the inegral test to show that =1 converges. 1+n2

A: To solve this question first we check derivative of function is negative for n&gt;0 and then we show…

Q: Use the Ratio Test to determine the radius of convergence R of Does it converge at the endpoints 2n…

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Q: What is the convergency interval of (2n)l

A: The given series is,  ∑n=1∞n!23n2n!xn To find its interval of convergence.

Q: Suppose that p(æ) > anx" converges on (-1, 1], find the internal of convergence of p(6x – 9). n=0

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Q: Show that the sequence of functions {f.} where f,(x)=nxe is non-uniformly convergent on [0,1]. (by…

A: Test for uniform convergence of sequences: Let fn be a sequence of functions such that it converges…

Q: Help please

A: Consider the given series:

Q: Use the integral test to show that the series 1 is convergent. (2n – 1)3 -

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Q: Prove that or 「+ X。- ズー 2. 71 number J2 Converged to

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Q: If a power series ∞ n=0 anxn converges absolutely at a pointx0, then it converges uniformly on the…

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Q: The integral S x3 converges to Select one: O True False

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Q: Suppose that p(x)=an" converges on (-1, 1], find the interval of convergen n=0 8 left end included…

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Q: 27 n! n=0 converges to 0. 8.

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Q: îf хи 1+nn } Convergent uniformy in [0,00) ?

A: Introduction: As a sequence of real numbers, a sequence of functions is also convergent or…

Q: Use the integral Test to determine if the series converges or diverges Be sure to prove all three…

A: The solution are next step

Q: Use the Integral Test to show that the series Σε. n=0 converges.

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Q: Integral

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Q: IUS IIIteTval of Converger Approximate In(0.5) using the first 5 terms using the expansion.

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Q: Use comparison test to show that the series E=1 (2) converges. 5n2-п.

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Q: Use the Limit Comparison Test to determine the convergence or divergence of the series.

A: Limit comparison test: Suppose we have two series ∑an and ∑bn . Define limn→∞anbn=L If L is positive…

Q: If |fn(x)| < an for all x and Ln=1 an converges, prove tha En-1 fn(x) converges uniformly. n=1

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Q: Find the pointwise limit f(x) for {nxe-nx} for x ∈ (0, +inf)). Does the sequence converge uniformly…

A: Given, fx=nxe-nx , x∈0,∞ Since, limn→∞fx=0 , ∀x x=0, fx=0 and e-nx→0 as n→∞ Let, fx converges…

Q: Find the interval of convergence of Ln=1 (r-1)" 2n

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Q: (e) $₁ = 5 and Sn+1 = √√4s +1 for n ≥ 1.

A: Given s1 = 5 and sn+1 = 4sn+1 for n≥1

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.