I have to solve - $$\sum_{i=1}^\infty \left(\frac{5}{12}\right)^i$$ - geometric series?
The geometric series sequence I know is - $$\sum_{i=0}^\infty x_i= \frac{1}{1-x}$$
However in my assignment, the series starts from $i=1$.
The solution I have is - $$\sum_{i=1}^\infty \left(\frac{5}{12}\right)^i = \frac{1}{1-\frac{5}{12}}-1$$
Can you explain please why is that the solution?
Answer
HINT:
$$\sum_{i=0}^\infty x_i= \frac{1}{1-x} =x_0 + \sum_{i=1}^\infty x_i$$
No comments:
Post a Comment