# Math Help - Prove

1. ## Prove

Prove that $(1+2+2^2+2^3+...+2^200) \vdots 7$

note :there is +...+2^200 ,problem with latex

2. Hello, beq!x !

What does the \vdots mean? . . . "is divisible by" ?
If so, I have a proof . . .

Prove that: . $1+2+2^2+2^3+ \hdots +2^{200}$ .is divisible by 7.

$N \;=\;(1 + 2 + 2^2) + (2^3+2^4+2^5) + (2^6+2^7+2^8) + \cdots + (2^{198} + 2^{199} + 2^{200})$

. . $=\;(1+2+4) + 2^3(1+2+4) + 2^6(1+2+4) + \cdots + 2^{198}(1+2+4)$

. . $=\; \underbrace{7\left(1 + 2^3 + 2^6 + 2^9 + \cdots + 2^{198}\right)}_{\text{a multiple of 7}}$

Therefore, $N$ is divisible by 7.

3. The code for $2^{200}$ is 2^{200} and the is divisible symbol $\mid$ is /mid.