JEE Main 202127 Aug, Morning shiftMathematicsEasySequence and Series179× since 2002If 0 < x < 1, then 32x2+53x3+74x4+.....{3 \over 2}{x^2} + {5 \over 3}{x^3} + {7 \over 4}{x^4} + .....23x2+35x3+47x4+....., is equal to :AOption A. x(1+x1−x)+loge(1−x)x\left( {{{1 + x} \over {1 - x}}} \right) + {\log _e}(1 - x)x(1−x1+x)+loge(1−x)BOption B. x(1−x1+x)+loge(1−x)x\left( {{{1 - x} \over {1 + x}}} \right) + {\log _e}(1 - x)x(1+x1−x)+loge(1−x)COption C. 1−x1+x+loge(1−x){{1 - x} \over {1 + x}} + {\log _e}(1 - x)1+x1−x+loge(1−x)DOption D. 1+x1−x+loge(1−x){{1 + x} \over {1 - x}} + {\log _e}(1 - x)1−x1+x+loge(1−x)CheckSkip · show solution
