You learned that Using this fact, find a power series representation for Full-screen Snip Select one: 3nz"+1 3nz" 3(n +1)z" n3"+1 (n+ 1)3"z"

Q: o Determine whether the series is FFLEPU comvergent divergent en 4. n(nti) A=t

A:

Q: (3x – 3)" is a power series centred at Answer:

A: Given that: ∑n=0∞(3x-3)n

Q: Determine whether the series converges or diverges. cosº (n) n² + 5 O converges O diverges

A: Here, the given series is: ∑n=1∞cos2(n)n2+5 Let, an=cos2(n)n2+5; n≥1

Q: Suastion 2 8, と what is the power Series expor sion と 1. -()け a)3 と 3 と-○ c)を

A:

Q: Does the series converge or diverge? If it converges, what is the sum? Show your work. Σ1-4…

A:

Q: Q2.Use n-th term test to test the series: E (-1)" /n+ Jn-Vn. n-1

A: To find- Use n-th term test to test the series: ∑n=1∞ -1nn + n - n     Test used-  The n-th term…

Q: tion 1- ]: ): Determine whether the series 1 Σ (2n- 1)4 n=1 M8

A: According to guidelines we solve one question.

Q: What is the power series representation of 2/((1-2x)^2)?

A: it's important to understand that the given function 2/((1-2x)^2) is a derivative of 1/(1 - 2x).…

Q: [MO22] Express as a single power series form: 00 3. > (n – 2)an+1(2x – 3)*1+ An-1(2x – 3)"-1 n32

A:

Q: Find the center and the radius of convergence of the power series (z – 2j)" n=0 Show the details of…

A:

Q: 3. For the SERIES determine whether it converges or diverges. If it converges, find n=0 the sum.

A:

Q: In Exercises 99–102,verify that the Ratio Test is inconclusive for the p-series. see the equation…

A: Verify that the Ratio Test is inconclusive for the p-series.           ∑n=1∞1n0.05

Q: 1" n=1 V 2n +n– 1

A:

Q: Find a power series representation of x3 (x + 2)

A: First I have written a power series for a well known function , just using them find the power…

Q: Use a substitution to shift the summation index so that the general term of the given power series…

A: Given : ∑n=1∞Cnnxn+4 We need to involve xk in place of xn+4 So, substitute n+4=k⇒n=k-4 So, the…

Q: What are the first four terms of a Maclaurin series for  y(x) = (1+ x)-3 ?

A: The Maclaurin series of a function f(x) is given by the following formula. fx=∑k=0∞fk0k!xk Where…

Q: 3. Show divergence or find the sum of the series -5 +32n 11" n3D2

A: Given: The series ∑n=2∞-5n+32n11n To determine: The divergence or sum of the series.

Q: (2n)! 5n+1(n!)2 n=1

A:

Q: S(z) = 64 –3 V/

A: f(x) =x964-x3We can rewrite the function as;f(x) = x9  164-x3f(x)=x9 (1641-x364)a=164,  r=x364…

Q: Find the power series representation and the radius of convergence for the representation.…

A: Given fx=x4ln3+12x2. Rewriting as fx=x4ln31+4x2fx=x4ln3+x4ln1+4x2

Q: Determine whether the series converges or diverges. 36n! Σ n = 1 converges O diverges

A:

Q: Determine whether this series converges or diverges by divergence test 00 Σ Зп 2 5n + 1 n=1

A:

Q: find a power series representation for this function?

A:

Q: Determine and justify whether the series is convergent or divergent.

A:

Q: a) ΣΣ п n=0

A:

Q: Determine whether the given series is convergent or divergent. Σ 2n2 + 9 n = 1 convergent O…

A: given sequence is                                                        ∑n=1∞n2n2+9 nth term is…

Q: (2n)! Σ (2n)!

A:

Q: Does the series from 1 to infinity of ((2n)!)/((n!)^2*5^n) convere or diverge using the ratio test?

A:

Q: State the test which applies to the series. Consider DCT/LCT as one test.

A:

Q: Determine whether the series converges or diverges. 2n n = 1 2 + 5" converges O diverges

A:

Q: 6. Use the alternating series test to determine whether the series E(-1)": Inn coverges. n=3

A: Given series is ∑n=3∞(-1)nln(n)n

Q: Evaluate the series or state that it diverges.

A: Given: S=∑k=0∞120.2k+320.8k for finding given summation, first we expand given expression so,…

Q: 2. Does the series converge or diverge? If it converges, find its sum. n² +n n=1

A: Given To find series convergence by using  comparison test .

Q: s converges or diverges.

A:

Q: Evaluate the series or state that it diverges. 3k Σ k=2

A:

Q: Determine whether the series (-1)"+1, n³ +1 n2 converges or diverges. n=1 Show all your work (and…

A: Given :

Q: Determine if the series is convergent or divergent. Show your work, and clearly state the test used…

A: Given series:  ∑n=1∞1(n+1)!-n! We have to check whether the series converges or diverges. Ratio test…

Q: Determine whether the alternating series converges or diverges

A: Check whether the series is convergent or divergent.

Q: Determine whether the series converges or diverges. n + 5 I 1 O converges O diverges

A:

Q: Determine whether the series converges or diverges. 3n2 1 4n° + 3 n = 3 converges O diverges

A: Given query is to find the series converges or diverges.

Q: Determine whether the series converges or diverges. 1 Σ 3n + 2 n = 1 converges O diverges

A:

Q: Express as a single power series form: У (Зп + 2)аn-1(х + 2)"+3 — У (5n - 2)а, (х + 2)"-1 n=-1 n=3…

A:

Q: Determine whether the series converges or diverges. Σ 2n + 4 n = 1 O converges O diverges

A:

Q: Find the sum of the series or show that it diverge n=1 4 3n+2 + 1 8n-2)

A:

Q: Determine whether the series converges or diverges. Σ e2/n n = 1 O converges O diverges

A: Given series is, ∑n=1∞e2/nn

Q: > Σ Write nCnxn+2 + (n- 1)C,x"-1 as one power series. | n=0 n=1

A:

Q: Find the sum of the series or show that it diverge 4 (a) Σn=1(3+2 + 8n-2

A:

Q: Is the series divergent or convergent? Show solution and explanation. +oo In n n2 n=2

A:

Q: Evaluate the series or state that it diverges.

A: rewriting the infinite series we have ∑k=2∞383k=∑k=2∞27512k

Q: Is the series divergent or convergent? With solution and explanation. +oo El-1)» (2n)! 2n n=1

A: