I was given the following question:
Calculate $$1-\frac12+\frac14-\frac18+\frac1{16}- \frac1{32}+\frac1{64}-\cdots -\frac1{512}+\cdots;$$ and express the answer as a simple fraction.
My approach was to use the following formula: $\frac1{1-r}$ where $r$ is the common ratio. In the end I got $2/3$. Am I correct?
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Also, how would i be able to explain this by words?