Sum of alternating series

How do you find the sum of a series with alternate signs. I know how to find with same signs but not alternating. I have no idea where to start. For example, 1-(1/3)+(1/5)-(1/7)+(1/9)...-(1/1003) with the sum equaling to 0.7849~pi/4

*This is not a homework problem. This is a studying question for my upcoming exam. I am very new to matlab and do not know where to start.

Answer 1

[Star Strider]

Just create the series and use the sum function:

N = 1003;
frc = (1./(1:2:N));
exv = (-1).^(0:numel(frc)-1);
ser = frc.*exv
ser_sum = sum(ser)

ser_sum =
   0.784900155923366   

Answer 2

[jeewan atwal]

Please go through following link:

https://www.quora.com/Why-is-1-1-3-+-1-5-1-7-+-1-9-%CF%80-4