Observe the following pattern `1=1/2{1xx(1+1)},` `1+2=1/2{2xx(2+1)},` `1+2+3=1/2{3xx(3+1)},` `1+2+3+4=1/2{4xx(4+1)}` and find the values of each of the following : `1+2+3+4+5++50,` `31+32++50`

Explanation

Observing the three numbers for right hand side of the equalities:
The first equality, whose biggest number on the LHS is `1`, has `1`, `1` and `1` as the three numbers.
The second equality, whose biggest number on the LHS is `2`, has `2`, `2` and `1` as the three numbers.
The third equality, whose biggest number on the LHS is `3`, has `3`, `3` and `1` as the three numbers.
The fourth equality, whose biggest number on the LHS is `4`, has `4`, `4` and `1` as the three numbers.
Hence, if the biggest number on the LHS is `n`, the three numbers on the RHS will be `n`, and `1`.
Using this property, we can calculate the sums for (i) as follows:(i)`1 + 2 + 3+. . . . . . . . +50 =1/2times50times(50 + 1) = 1275`.