1. Determine if the series converges or diverges and state the test used. a. E-1 22n31-n Inn b. Σ-1 c. En=1 2n2+4n+3 d. En=1 (-1)"3n 4п-1 e. En=1 n 3n+2 2n+

Q: Determine whether or not the series converges

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Q: 9. The values of p for which the series is convergent (n') using the integral test are a) p>1 C) p21…

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Q: 2. Determine if the series converges absolutely, c a. E-1(-1)" (-1)7-1 c. E=1(-1)" n+2

A: These series are alternating series test  So for convergence first we apply this test  In which if…

Q: (c) Which of the following series converge? Justify any assertions that you make. (1) 3n (ii) n+1 3n…

A: I have given all the solution with the help of different tests.Final solution is in boxes.

Q: 25. Choose the series that is convergent: ΑΣ A) 1+ n n+1 B ) Σ- 2 n n 4n n1 ο Σ7m 3 n n 2 D Σν+1 +4n…

A: In order to identify the convergence of series from given options, apply the divergence tests as…

Q: IV. Determine whether the given series is convergent or divergent. Justify your answers. 1 (2n)! (a)…

A: Note: Since you ask multiple question, only first question will be addressed here. It is given that,…

Q: Use any method to determine whether the series converge. (a) E 4k k=1 The series (b) E 4k + 1 k=1…

A:

Q: 1. Use the Root Test to determine if the series (-1)" 2/n en? (2n² – 1)" n=1 converges or diverges.

A: Solution:-

Q: 4. Determine if the infinite series diverges or converges. a. E2 b. En1 (n+1)2-1 3n+1 4n+2 C. c. E…

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Q: Determine whether the alternating series converges. 31n k Σ(-1) k k=3 The series diverges.

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Q: (2) Compute 2" - 3n+2 5n-1 n=4 by explaining clearly why the series converges, and then actually…

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Q: Express the series using sigma notation 6m + 3m + 0 + (-3m) + (-6m)... E-3bn +9b E-3bn – 9b E-3bn…

A: Use the expression form the summation form

Q: 1 Use the comparison test to determine whether the series converges or diverges. (3n + 1)15 n=1

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Q: Q1) Which of the series converge, and which diverge? Give reasons for your answers. In(n2) 1 ) Σn-2…

A: Series test

Q: -n 5n² – 2n + 1 00 - Determine whether the series converges or diverges. Show all your work. Зп? + п…

A:

Q: 2. Determine if the following series converges or diverges. n' + 3n? + 5 b. E а. n 5n8 - Зп — 4 n=1…

A: 1) the given series is  (n4+3n2+5)/(5n6-3n-4)  2)n/en^2.

Q: > 9( – 1.2)* is an alternating geometric series, which convergesO diverges. k=0 E 9( – 1.2)* = k=0…

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Q: 4.) Determine Hthe given series converges or diverges C.) E n*rn +2 (3)"

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Q: +oo 1 (2n)! ( a) Σ ( c) Σ-1)" 4n2 – 8n + 3 n=1 2" n=1 +00 In n (b) Σ-1)" n2 n=2

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Q: 12) Determine whether the series converges absolutely or conditionally, or diverges: (-1)n+1 nyn…

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Q: Q1 Find a formula for the nth partial sum of this Telescoping series and use it to determine whether…

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Q: 2n Determine whether the series converges or diverges. Ln=1 n2 +n

A: The given series is ∑n=1∞2nn2+n.   Rewrite the given series as follows. ∑n=1∞2nn2+n=2∑n=1∞nn2+n…

Q: 23. Choose the series that converges: 2" b) Σ (n+1)! Θ ΣΙ2--] 3 Ο Σ 2 n-1 n=1 n-0 1 d) ο Σ n e) n=1…

A: a) Here, we find first few partial sum ,since lim sn as n approaches infinity does not exist.…

Q: Determine whether the given series converges or diverges: 00 S(2n)! (n!)2 n=1

A: The ratio test states that: if L < 1 then the series converges absolutely; if L > 1 then the…

Q: Q3: Which of the series and sequences converges and which diverges? 3- E=1 enz 13D1 4- an = 1+ (-1)…

A: We have to find which of the series and sequence converges or which diverges.

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

A:

Q: (a) 1 5+ 27 n=1 (b) Зп + 3 25n - 1 n=1

A: Solution

Q: 5. Determine whether the series converges or diverges. b. Σ... (1+2n)" a ΤΟ n=1

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Q: Determine if the series converges.

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Q: Determine if is a p-series or not. If so, determine if the series converges or 7 5ni n=1 diverges,…

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Q: Q1) Which of the series converge, and which diverge? Give reasons for your answers. -2 In(n2) 1)…

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Q: n=1 b) Use the Ratio Test to determine if the series converges or diverges. n5" L(2n + 3)ln (n + 1)…

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Q: Determine if the given series is convergent or divergent. (1 – 2n²)" Σ 1. n2n n=1

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Q: How can I determine whether the series (-1)n+1e(-1/n+1) absolutely or conditionally converges or…

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Q: 15. Determine which of the following alternating series converge and which diverge. Justify your…

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Q: Determine whether the series converges or diverges. 12n2 - 8 4 n + 7 n = 1

A: Given: un=12n2-8n4+7 To prove that the given series is convergent or divergent Limit Convergent…

Q: 5) Find the values of a so that the power series (-1)"- n2. 3n converges. n=1

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Q: Determine whether the series converges or diverges: k3 3k k=1

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Q: Determine whether the series converges or diverges. E(-1)n + 1. n* + 16 n = 1 1.

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Q: 4. Use the Ratio Test to determine if each of the following series converges or diverges. You do not…

A: We have to use ratio test.

Q: 1. Determine if the following series converges or diverges and justify your claim: -1)" /ñ (3n)! (n*…

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Q: 2. Determine if the following series converge or diverge. Explain your answer. ( a) Σ ( n%31 (b) E=2…

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Q: E. Determine the convergence or divergence of the series. n2+1 2n2+1

A: determine whether the given series is convergent or divergent

Q: 00 Find the interval of convergence of the power series (a) xn (х — 4)" (b) n· 2n n + 2 n=0 n=0

A: Here we have to find the interval of the convergence of the given power series.

Q: 2. Show that the series is conditionally convergent: n 2(-1)"-1, n2 1 n=2 For what values of p does…

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Q: 10.) Determine whether the series converges conditionally or absolutely, or diverges (-1)" e¬n² =0

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Q: 00 2) 3) n3+5n²-17 n en n n=1 n =2

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Q: Determine whether the series converges, and if so find its sum. 4k+2 2 7k-1 k=1

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Q: Q.4. Use the Ratio Test to determine if the following series converges or diverges. n! Σ=1 (2n+1)!

A: To find whether the given series converges or diverges.

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.