Evaluate the infinite geometric series 0.79 + 0.079 + 0.0079 + 0.00079 + 0.000079 + \dotsb. Express your answer as a fraction.
The fraction is 7990
sum s=(7.9∗10−1)⏟=a+(7.9∗10−1)∗10−1+(7.9∗10−1)∗10−2+(7.9∗10−1)∗10−3+⋯+(7.9∗10−1)∗10−(n−1) $$ r=(7.9∗10−1)∗10−1(7.9∗10−1)=10−1 $$ s=a1−r=(7.9∗10−1)1−10−1 $$ s=(7.9∗10−1)1−10−1∗101101 $$ s=7.9101−1=7.99 $$ s=7.99=0.87777777777777777777777777¯7=0.8¯7
sorry, but what is the fraction for this?
thank you so much Heureka!
