Question

Suppose that Achilles runs 10 times as fast as the tortoise and that Achilles runs 10 yards a second. Suppose that the initial distance between Achilles and the tortoise is 100 yards. Then Achilles runs successively 100 yards, 10 yards, 1 yard, 1 10 yard, and so on. Find the total number of yards Achilles must travel in order to catch his competitor and find the total number of yards the tortoise must travel, by using the geometric series that you learned in Calculus.

Answer 1

Answer and Step-by-step explanation:

Achilles runs 100 yards, but the tortoise runs 10 yards.

Achilles runs 10 yards, and the tortoise is 1 yard ahead.

Achilles runs the yards, and the tortoise runs 1/10 yards.

Achilles runs 1/10th yards, but the tortoise run1/100 yards.

This is the concept of limit of infinite series, shows that

10 + 1 + 1/10 + 1/100 + 1/1000 + …

=11.111….

Total time  take Achilles to catch up in seconds,

It was evident between 11 1st 12. As we know that 0.33333 … = 1/3

Dividing both sides by 3, we get

0.11111…. = 1/9

Hence, Achilles needs 11 and 1/9 sec to catch up.

In more formal notation, Achilles needs time to catch up is:

∑n=0∞ = 10 + 1 + 1/10 + 1/100 + 1/000 + …= 11 1/9