How do I solve this and what's the anwser

1. Using an infinite geometric series, show that 0.9999999... = 1 0o 2. Show that _ 2 3 diverges. n=1 3. Each morning, a patient receives a 25 mg injection of an anti-inflammatory drug, and 40% of the drug remains in the body after 24 hours. Find the quantity in the body: a. After the 3rd injection. b. After the 6th injection. c. in the long run, right after an injection. 00 4. Let the sum of the the infinite series EGT =S k= 1 a. Show that S = n b. Let the finite series be E () . Find n such that the S - S