What is the sum of the first 10 terms of the geometric progression $1,2,4,8,\dots$?

Solution

1. Identify the parameters of the geometric progression: the first term $a=1$, the common ratio $r=2$, and the number of terms $n=10$.
2. Use the sum formula for a geometric progression: $S_n=\frac{a(r^n-1)}{r-1}$.
3. Substitute the values into the formula: $S_{10}=\frac{1(2^{10}-1)}{2-1}$.
4. Calculate the result: $$\begin{array}{rl}{S}_{10}& =1024-1\\ & =1023\end{array}$$.
5. Hence the answer is (B).