+0  
 
0
36
1
avatar

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
Sort: 

1+0 Answers

 #1
avatar
+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

14 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details