Limits Continuity And Differentiability

\(\mathop {\lim }\limits_{n \to \infty } \left[ {\left( {{1 \over {2\,.\,3}} + {1 \over {{2^2}\,.\,3}}} \right) + \left( {{1 \over {{2^2}\,.\,{3^2}}} + {1 \over {{2^3}\,.\,{3^2}}}} \right)\, + \,...\, + \,\left( {{2 \over {{2^n}\,.\,{3^n}}} + {1 \over {{2^{n + 1}}\,.\,3n}}} \right)} \right]\) এর মান