JEE Main 202124 Feb, Evening shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002If n≥2n \ge 2n≥2 is a positive integer, then the sum of the series n+1C2+2(2C2+3C2+4C2+...+nC2){}^{n + 1}{C_2} + 2\left( {{}^2{C_2} + {}^3{C_2} + {}^4{C_2} + ... + {}^n{C_2}} \right)n+1C2+2(2C2+3C2+4C2+...+nC2) is :AOption A. n(2n+1)(3n+1)6{{n(2n + 1)(3n + 1)} \over 6}6n(2n+1)(3n+1)BOption B. n(n+1)(2n+1)6{{n(n + 1)(2n + 1)} \over 6}6n(n+1)(2n+1)COption C. n(n+1)2(n+2)12{{n{{(n + 1)}^2}(n + 2)} \over {12}}12n(n+1)2(n+2)DOption D. n(n−1)(2n+1)6{{n(n - 1)(2n + 1)} \over 6}6n(n−1)(2n+1)CheckSkip · show solution
