This is LaTeX code:

[latex]
1 - f_2 \left( {n_1 ,n_2 } \right) = \left( {p_1 p} \right)^{n_1 + 1} + \left( {p_1 p} \right)^{n_2 + 1} - p_2 p^2 \left( {2p_1 - 1} \right)\left( {p_1 p} \right)^{n_1 + n_2 }
[/latex]