Hi, below are the photos of the question

plz answer all questions and there is no need to give the explanation for the answer just fill the right blanks

thanks

Also, make sure the answers are right

1. [-/1 Points] DETAILS LARCALC12 9.1.031. MY NOTES ASK YOUR TEACHER Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. (If the quantity diverges, enter DIVERGES.) an = (-1)0 n n+ Need Help? Read It Watch It11. [-/1 Points] DETAILS LARCALC12 9.2.030. Find the sum of the convergent series. n n = 012. [-/1 Points] DETAILS LARCALC12 9.2.031. Find the sum of the convergent series. 8 n(n + 2) n= 114. [-/2 Points] DETAILS LARCALC12 9.6.019.MI. MY NOTES ASK YOUR TEACHER Consider the following series. (n - 1)! n = on Using the Ratio Test, find the following limit. (If the limit is infinite, enter 'co' or '-co', as appropriate. If the limit does not otherwise exist, enter DNE.) lim an + 1 n - 0 an Determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods. converges O diverges15. [-/2 Points] I DETAILS I LARCALC12 9.6.032. I MY NOTES Consider the following series. Determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods. C0 nve rges diverges 2. [-/2 Points] DETAILS LARCALC12 9.2.039.MI. Consider the following repeating decimal. 0.8 (a) Write the repeating decimal as a geometric series. n = 0 (b) Write the sum of the series as the ratio of two integers. Need Help? Read It Master It3. [-/3 Points] DETAILS LARCALC12 9.2.044. Consider the following repeating decimal. 0.417 (a) Write the repeating decimal as a geometric series. 0.417 : + n = 0 (b) Write the sum of the series as the ratio of two integers. Need Help? Read It5. [-l2 Points] DETAILS LARCALC12 9.6.025. MY NOTES I ASK YOUR TEACHER I l PRACTICI Consider the following series. on n3 n n=14 Using the Ratio Test, find the fol owing limit. (If the limit is infinite, enter 'oe' or '-oo', as appropriate. If the limit does not otherwise exist, enter DNE.) _ a lim npco n+1'= an Determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods. converges diverges Need Help? 6. [-/2 Points] DETAILS LARCALC12 9.6.049. MY NOTES ASK YOUR TEACHER Consider the following series. Using the Root Test, find the following limit. (If the limit is infinite, enter 'co' or '-co', as appropriate. If the limit does not otherwise exist, enter DNE.) lim V lal Determine the convergence or divergence of the series. If the Root Test is inconclusive, determine the convergence or divergence of the series using other methods. O converges diverges7. [-/1 Points] DETAILS LARCALC12 9.7.032.MI. Find the oth Taylor polynomial for the function, centered at c. f(x) = x cos(x), n = 2, C = 1 P, (x) =8. [-I1 Points] | DETAILS I LARCALC129.8.012.M|. MYN Find the radius of convergence of the power series. (If you need to use so or m, enter INFINITY or INFINITY, respectively.) 9. [-12 Points] | DETAILS I LARCALC129.9.004. Find a geometric power series for the function, centered at 0, by the following methods. 3 x): 4+X (a) by first writing f(x) in the form and then finding the power series 1r mam) n=0 (b) by long division (Give the first three terms.)