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.
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!!.