Solve the Problem $0.77 \overline { 7 }$ As an Infinite Geometric Series and Use the Formula For an Infinite

Multiple Choice

Solve the problem.
-Write $0.77 \overline { 7 }$ as an infinite geometric series and use the formula for $\mathrm { S } _ { \infty }$ to write it as a rational number.

A) $\frac { 7 } { 100 }$
B) $\frac { 7 } { 10 }$
C) $\frac { 70 } { 9 }$
D) $\frac { 7 } { 9 }$