Tính giá trị của biểu thức \(T = \log \left[ {\frac{{f(96) – f(69) – 241}}{2}} \right]\)

\(\begin{array}{l}n = 1 \Rightarrow f(m + 1) = f(m) + f(1) + m.1 \Leftrightarrow f(m + 1) = f(m) + m + 1\\ \Leftrightarrow f(m + 1) – f(m) = m + 1\\ \Rightarrow f\left( {96} \right) – f\left( {69} \right) = \left[ {f\left( {96} \right) – f\left( {95} \right)} \right] + \left[ {f\left( {95} \right) – f\left( {94} \right)} \right] + … + \left[ {f\left( {70} \right) – f\left( {69} \right)} \right]\\\;\; = 96 + 95 + … + 70 = \frac{{27.\left( {96 + 70} \right)}}{2} = 2241\\ \Rightarrow \frac{{f(96) – f(69) – 241}}{2} = \frac{{2241 – 241}}{2} = 1000\\ \Rightarrow T = \log \left[ {\frac{{f(96) – f(69) – 241}}{2}} \right] = \log 1000 = 3.\end{array}\)