Series

If the sequence a1,a2,a3,a4,......anform an A.P. Then value of a12 - a22 + a32 -a42  +.....+a2n-12  - a2n2   is

[n/(2n-1)] [ a12 - a2n2] . If we rearrange the terms-(a12 - a22 )+ (a32 -a42  )+.....+(a2n-12  - a2n2  ) which are up to n terms. Each expression under bracket can be put as A1+A2+A3+...._An where A1=(a12 - a22 ), A2=(a32 -a42  ) etc and A1,A2,..... are in AP & common difference=square root of (A1-A2)/4.
       a1(only an integer)
      Common Difference
      No. of terms (n)
 
series is : - +-+- up to 2n terms  
Last term
Sum of the series up to n terms
Sum of the series up to 2n-1 terms
Sum of the series up to 2n terms