$$\sum_{k=0}^{6}{ $2^{k}$}$$
You asked:
Evaluate the expression: \(\sum_{k = 0}^{6} {{2}^{k}}\)
MathBot Answer:
\[\sum_{k=0}^{6} 2^{k} = 127\]
$$\begin{aligned}\sum_{k=0}^{6} 2^{k} &= \frac{\left(1 - 2^{1 + 6}\right)}{\left(1 - 2\right)} \ \ \ \small{\color{grey}\text{by the identity} \sum_{n=0}^{m} a^n = \frac{1-a^{m+1}}{1-a}}\\&= \left(-127\right) \left(-1\right)\\&= 127\end{aligned}$$