Question

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. K-1 2 (0)" k = 1 Select the correct choice below and fill in any answer boxes within your choice. O A. The series converges. The sum of the series is (Type an integer or a simplified fraction.) B. The series diverges.

Answer 1

Geometric series:- A geometric series with common ratio & and first term a the sum of 7th terms sn = a (on-1) 8 - 1 a Soo 1-8

infinite consider, the geometric series K-, 29 70)* k=1 7 up to -) 7 up to o let sn= 1 + 2 + ( 3 ) + ( ) + Here, a=1 & ( Sn 0 (71) (19)") Ź - 1 6). 2 7 98 no

- 3 Sn = 11 ة ام 2 2 1-3 3 3 3 Sn od 2 Therefore 2 2 2704)*7*2 kr/ 2/ - 10.5 Σ 7 k=1 2 correct answer is A Hence, sum of the A series converges. The The series 21 2