Evaluate the value of the expression
\sum_{k=T_{24}+1}^{T_{25}} k
where T_{i} denotes the i^{\text {th }} triangular number (the sum of the integers from 1 through i ).
Evaluate the value of the expression
where T_{i} denotes the i^{\text {th }} triangular number (the sum of the integers from 1 through i ).