A sum in which subsequence terms cancel each other and leave only first and last term is called as telescoping sum.

Example:    ∑ (a_i - a_i+1 )   where (1<= i <=n-1)

              = (a₁ - a₂ ) + (a₂  - a₃ ) + (a₃ - a₄ ) +..............+ (a_n-2 - a_n-1 ) + (a_n-1 - a_n )   

             = a₁ - a_n