GATE 2021 BT – Question 30
The sum $1+1/3+1/3^2+1/3^3+\cdots$ (one decimal place) is _______.
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Show answer and explanation
Correct answer: 1.49 to 1.51
Explanation
This is an infinite geometric series with first term $a=1$ and common ratio $r=\dfrac13$. Since $|r|<1$ it converges:
$$S=\frac{a}{1-r}=\frac{1}{1-\frac13}=\frac{1}{\frac23}=\frac32=\mathbf{1.5}.$$