Question

the wavelength of series limit for lyman series for he^+ ion would be

Answer 1

I didn't know they had a lyman series for He+, the more you know.
What makes a series lyman is that it ends up in the n=1 state. It can start from n=5, but as long as it jumps to n=1, it is a lyman series.

The balmer series are transitions that end with n=2.

The longest wavelength correspond to the lowest energy, so I expect it to have the smallest jump, and for lyman series, it's obviously the jump from n=2 to n=1.

You can look up the experimental values or use the rydberg formula, but you should get an answer of about 122nm