Value of the Series

Take a good look at the following series:

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

Find the values of the series and multiply the answer by 4. You will notice that a well –known value approximates this product. Even more interesting is that as you add more terms the approximation becomes closer.

Answer: 

 II – The value of the given series is approximately 0.76. And when two more terms are added the value approximates to 0.77. When we multiply these values by 4, we get 3.04 and 3.08. If this is repeated indefinitely we shall approach the value of 3.14

3.14 is the value of II correct to two places of decimals.