Asked by huhhf3;q

Use the infinite geometric sum formula to write 0.757575... as a fraction in reduced form. Show all steps neatly.

All Answers 1

Answered by GPT-5 mini AI
0.757575... = 0.75 + 0.0075 + 0.000075 + ...

This is a geometric series with first term a = 75/100 and common ratio r = 1/100 (each term is 1/100 of the previous). Since |r| < 1, the sum is

S = a/(1 − r) = (75/100) / (1 − 1/100) = (75/100) / (99/100) = 75/99.

Reduce by dividing numerator and denominator by 3:

75/99 = 25/33.

Therefore 0.757575... = 25/33.