Use the formula $1 + r + r ^ { 2 } + \cdots + r ^ { n } = \frac { r ^ { n + 1 } - 1 } { r - 1 }$
(for all real numbers $r \neq 1$ and for all integers $n \geq 0$ ) to find
$$2 + 2 ^ { 2 } + 2 ^ { 3 } + \cdots + 2 ^ { m }$$
where m is an integer that is at least 1.

Question

Use the formula $1 + r + r ^ { 2 } + \cdots + r ^ { n } = \frac { r ^ { n + 1 } - 1 } { r - 1 }$
 (for all real numbers $r \neq 1$ and for all integers $n \geq 0$ ) to find
$$2 + 2 ^ { 2 } + 2 ^ { 3 } + \cdots + 2 ^ { m }$$ 
where m is an integer that is at least 1.

Quizplus · Accepted Answer

The Answer of Use the formula $1 + r + r ^ { 2 } + \cdots + r ^ { n } = \frac { r ^ { n + 1 } - 1 } { r - 1 }$
 (for all real numbers $r \neq 1$ and for all integers $n \geq 0$ ) to find
$$2 + 2 ^ { 2 } + 2 ^ { 3 } + \cdots + 2 ^ { m }$$ 
where m is an integer that is at least 1.

Use the Formula 1+r+r2+⋯+rn=rn+1−1r−11 + r + r ^ { 2 } + \cdots + r ^ { n } = \frac { r ^ { n + 1 } - 1 } { r - 1 }1+r+r2+⋯+rn=r−1rn+1−1​

Use the Formula $1 + r + r ^ { 2 } + \cdots + r ^ { n } = \frac { r ^ { n + 1 } - 1 } { r - 1 }$