In the sequence of sets $\left\{1\right\},\left\{2,3\right\},\left\{4,5,6\right\},\left\{7,8,9,10\right\},...$ the sum of elements in the 50^th set is

Last term in 2^nd bracket =1+2

Last term in the 3^rd bracket=1+2+3

Last term in the 50^th bracket=1+2+3+…+50=1275

50^th bracket contains 50terms 1226+…+1275

$=\frac{50}{2}\left[1226+1275\right]$

$=25\left[2501\right]$

$=62525$