Verifying Divergence Use the result of Exercise 64 to show that each series diverges.
(a)
(b)
(c)
(d)
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- (-1)"-1 6. (a) Show that the series is convergent. n2 n=1 (-1)"-1 (b) Find the partial sum s, of the series Estimate the error in using s; as an n2 n=1 approximation to the sum of the series. (c) Find a value of n so that s, is within 0.001 of the sum.arrow_forwardUse the power series f(x) = n=0 to determine a power series for the function, centered at 0, 14 d² (x+1)³ dx²x n=0 f(x) X- Need Help? (-1)"x", Ixl < 1 Determine the interval of convergence. (Enter your answer using interval notation.) (-1,1) Read It Watch Itarrow_forwardtan-ln | Consider the series n² +1 n=1 Is it true that the Integral Test can be used to determine the convergence or divergence of this series? [ Select ] Is the series convergent or is it divergent? [Select ]arrow_forward
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- Use Taylor series you already know to find the Taylor series generated by f(x) = x° sin(2x) at x = 0. Taylor series is n=0arrow_forwardTest the series for convergence or divergence. (-1)" + 1 4n4 n= 1 converges diverges If the series is convergent, use the Alternating Series Estimation Theorem to determine how many terms we need to add in order to find the sum with an error less than 0.00005. (If the quantity diverges, enter DIVERGES.) terms Submit Answerarrow_forwardConsider the geometric series 00 >G) (x - 3)" n=0 Find the values of x for which the series converges. Find the sum of the series (as a function of x) for those values of x found in (a).arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage