JEE Main 202126 Aug, Morning shiftMathematicsEasySequence and Series179× since 2002The sum of the series 1x+1+2x2+1+22x4+1+......+2100x2100+1{1 \over {x + 1}} + {2 \over {{x^2} + 1}} + {{{2^2}} \over {{x^4} + 1}} + ...... + {{{2^{100}}} \over {{x^{{2^{100}}}} + 1}}x+11+x2+12+x4+122+......+x2100+12100 when x = 2 is :AOption A. 1+21014101−11 + {{{2^{101}}} \over {{4^{101}} - 1}}1+4101−12101BOption B. 1+21004101−11 + {{{2^{100}}} \over {{4^{101}} - 1}}1+4101−12100COption C. 1−21004100−11 - {{{2^{100}}} \over {{4^{100}} - 1}}1−4100−12100DOption D. 1−21012400−11 - {{{2^{101}}} \over {{2^{400}} - 1}}1−2400−12101CheckSkip · show solution
