Find the sum to infinity of the geometric series $1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + ...$
A$\frac{3}{2}$CORRECT
B$\frac{2}{3}$
C$3$
D$\frac{1}{2}$
GCEFurther MathematicsSequences and Series2023
AI
Toaster Teacher
Why the answer is A, and why the others tempt you.
The sum to infinity of a G.P. is S = a/(1 - r), where |r| < 1. Here a = 1 and r = 1/3. So S = 1/(1 - 1/3) = 1/(2/3) = 3/2. Option B (2/3) is the value of (1 - r) mistakenly taken as the answer, while option C results from not subtracting r from 1.
Want this in Pidgin, Yoruba, Igbo or Hausa? Sign up free →
Practice more Further Mathematics questions
GCE Further Mathematics has thousands more questions like this — with Worked answers on every one.