What do the following two sequences have in common?

78539816339744830961566084581988....... and

1, - 1/3, + 1/5, -1/7, +1/9, -1/11, + 1/13, -1/15....

Any help would be appreciated. Thank you.

Guest Jul 22, 2017

#1**+1 **

This one is easy to see! The first sequence is the result of evaluating the second sequence, which is called the Leibniz's formula for Pi. That is: 1- 1/3 + 1/5 -1/7 + 1/9 -1/11 + 1/13 - 1/15.......to infinity = Pi/4. So if we divide Pi by 4 =0.78539816339744830961566084581988.....except in your first sequence the "decimal point" has been removed to make a little more difficult to recognize. However, this Leibniz's formula converges extremely slowly. To get the first ten accurate digits, you will have to evaluate about 5 billion terms!!.

Guest Jul 22, 2017