10) Test the series for -n 8 7(e) n=T convergence bn = 7 en Compute the derivative: d bn. dn Since d bn dn the sequence is eventually always ²1 is eventually always 21 is eventually always 20 is eventually always >0 keeps changing sign or divergence Use alternating series The alternating series tells us is eventually monoton is not monotone the series converges the series diverges nothing

Q: Differentiate the series represented by the function f below term-by-term to find the power series…

A:

Q: 23, 24, 25, 26, 27, 28, 29, 30, 31, and 32 Determine whether the geometric series is co divergent.…

A: The series is: 3-4+163-649+ . . . To Do: We have to determine whether the given geometric series is…

Q: 21. Find the sum of the series 100 +90 +80 ... -50, when n =16. a. 2800 b. 1600 c. 800 d. 400

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Q: Question 13 A What are all values of x for which the series converges? A All xexcept x= 0 B |X/ = 3…

A: we have to find the value of X

Q: 1+3n 4. Σ=1 2n algebraically simplify b

A: I have explained everything with in the solution. Please go through that.

Q: To test the series n=1 series, so we could also investigate convergence using other methods.) of…

A: We need to evaluate ∫1∞e-4xdx

Q: cos(nn) Σ The series is convergent. n2 n=1 True False

A:

Q: Given the power series 2 2n A x(n + 3) n = 0 Use the technique that we covered in this unit to Shift…

A: To shift the index of the power series use the substitution n = R - 3

Q: ∞ ∞ o) If the series an is convergent, then arctan(1 + an) is divergent. n=1 n=1 Final Answer This…

A:

Q: Represent the function 1x as a power series f(x) = > 2+x n=0 Co C1 = C2 = C3 = C4 = Find the radius…

A: Let gx=x2+x Rewrite the function as  gx=x21+x2