Question

Calculate the sum of the infinite series S ∞=5-3+9/5-…A.)not possible B.)31/8C.)25/8D.)21/8

Answer 1

Looking at the series, we have a geometric sequence, where the first term is a1 = 5 and the common ratio is q = -3/5.

(This ratio can be calculated by dividing one term by the term before)

To find the sum of an infinite geometric sequence, we can use the formula below:

`S_(\infty)=(a_1)/(1-q)`

Since a1 = 5 and q = -3/5, we have:

`S_(\infty)=(5)/(1-(-(3)/(5)))=(5)/(1+(3)/(5))=(5)/((8)/(5))=5\cdot(5)/(8)=(25)/(8)`

Therefore the correct option is C.