Calculation of different types of maximum possible radiations which can be observed in (from higher energy level to lower energy level)

Explanation

`n _(2) =n, " "n _(1) =1`
Total no. of radiatin obtained having difference wave lengths = Trsnsition ending at `1 ^(st)` level + Transite ending at `2 ^(nd)` level …………..Transition ending at (n-1) energy levels.
= Total no. of radiation in lyman series + total no. of radiation in Balmer series `...................+ `Total no. of radiation in` (n – 1)` series.
`= (n-1) + (n-2) + (n-3) ...........+2+1`
`implies ((n -1) (n -1+1))/(2) implies (n (n-1))/(2)`