Final answer:
The sum of the infinite geometric series 7/10 + 7/100 + 7/1000 + ... is 7/9, calculated using the formula for the sum of an infinite geometric series.
Step-by-step explanation:
The student has asked us to compute the infinite sum 7/10 + 7/100 + 7/1000 + 7/10000 + ... . This series is a geometric series where each term is one-tenth the previous term. To find the sum of an infinite geometric series, we use the formula S = a / (1 - r), where 'S' is the sum of the series, 'a' is the first term, and 'r' is the common ratio between the terms of the series.
In this case, the first term 'a' is 7/10, and the common ratio 'r' is 1/10. Plugging these values into the formula, we get S = (7/10) / (1 - 1/10) = (7/10) / (9/10) = 7/9. So, the sum of the infinite series is 7/9.