please explain them step by step carefully paper with pen...because it's hard to understand keyboard typed solutions...Thank you

LIZ DETAILS ractice Another Consider the following repeating decimal. 0:819 (a) Write the repeating decimal as a geometric series. 0.819 + E n = 0 (b) Write the sum of the series as the ratio of two integers. Check Score21 [12. 5/12. 5 Points] _ETAILS _REVIOUS _NSWERS LARCALC'H 9,2 027, \" g V , Consider the following. 2 7(0 8)"'1 n=1 ' ,' , i (a) Find the sum of the series. l 5\": 35 4 (b) Use a graphing utility to find the indicated partial sum and complete \\the table. (Round your answers to four decimal places.) , ' ' f r \"T 1,0 20 50 100 1., \"31.2419 1 W b45966 9 W [34.9995 [V I l3499999 |,/ ' j. w 0 9,2: a O HW 9.6 - 2023SP MATH-2414-11 X *Homework Help - Q&A from Onl x + C webassign.net/web/Student/Assignment-Responses/last?dep=31571941 Check Score Hide Answer Use the Ratio Test to 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 -co, enter INFINITY or =INFINITY, respectively.) (-1)n+ In! n = 0 1 . 7 . 13 . . . (6n + 1) lim an + 1 = 1/6 -+ 00 converges O diverges Need Help? Watch It Submit Answer6. [14.28/14.28 Points] DETAILS PREVIOUS ANSWERS LARCALC11 9.7.028. Find the nth Taylor polynomial for the function, centered at c. F ( x ) = _ x2 ' n = 4, c = 5 1 2 3 PA(x) = 125 ( x - 5 ) + 625 (X - 5)2 - 4 25 3125 (X - 5) + 3125 (x - 5) 4 7. [14.32/14.32 Points] DETAILS PREVIOUS ANSWERS LARCALC11 9.7.031. Find the nth Taylor polynomial for the function, centered at c. f( x) = In(x), n = 4, c=2 Pa ( x ) - In ( 2 ) + 2 (x - 2 ) - 8 (x - 2)2 + 7(x - 2)3 - 2 64 (x - 2) 4 Need Help? Watch It