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To test the series e 2n for convergence, you can use the Integral Test. (This is also a geometric series, so we could n=1 alsCompute the value of the following improper integral, if it converges. (If it diverges, enter oo if it diverges to infinity,Compute the value of the improper integral. (If the integral diverges to oo, type oo; if the integral diverges to - oo, type, type -oo; if it Compute the value of the improper integral. (If the integral diverges to oo, type oo; if it diverges to- diTo test the series for convergence, you can use the P-test. (You could also use the Integral Test, as is the case k=1 with alTo test the series for convergence, you can use the P-test. (You could also use the Integral Test, as is the case k1 1.3 withEstimate the error in using the partial sum of 25 terms of the series Error < PreviewFind the smallest number n of terms needed to obtain an approximation of the series 27 accurate to 10 -4. n =Find the smallest number n of terms needed to obtain an approximation of the series 26ke .lok accurate to 10-6 k=1 n =To test this series for convergence * 3 +1 251 You could use the Limit Comparison Test, comparing it to the series ph whereTo test this series for convergence You could use the Limit Comparison Test, comparing it to the series where p= Preview np nTo test the series 210 for convergence, you will use the Limit Comparison Test, comparing it to the p series 2k8 11 Στο whereWe want to use the Basic Comparison Test (sometimes called the Direct Comparison Test or just the Comparison Test) to determi

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Llow since 18 finite henece Jae-in da - [-e-br] - [ 0-56-62) -- [o-ery e-2x dn= (-e-2)= e = 262 co Hence 150 e-2x da yako (fiIT poo 3lnadu 3rd dazo (-3)<a n2 alow by Cenchy integral Test (calculataled above). has finite limite slence et enx da is con@ dlence the series nel lanz Leo S, O Pixiz dx = 3 fant ()],0 - 3 (tant (oo) -tan 4(1) =3[ 77 - 7/4] = 391/4 < si na dn = 37

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