Sum to n terms of the series 1 + (1+x) + (1+x+x2) + (1+x+x2+x3) + .... Share with your friends Share 0 Muskaan Talwar answered this Dear Student, The nth term of given series will be 1+x+x2+...+xn-1Let Pn: 1+1+x+1+x+x2+...+1+x+x2+...+xn-1=n+n-1x+n-2x2+...+2xn-2+xn-1Now P1: 1=1 which is true.Thus result holds for n=1.Let the result hold for n=k. 1+1+x+1+x+x2+...+1+x+x2+...+xk-1=k+k-1x+k-2x2+...+2xk-2+xk-1For Pk+11+1+x+1+x+x2+...+1+x+x2+...+xk-1+1+x+x2+...+xk-1+xk=k+k-1x+k-2x2+...+2xk-2+xk-1+1+x+x2+...+xk-1+xk=k+1+kx+k-1x2+...+2xk-1+xkThus result is true for n=k+1 whenever it is true for n=k.Hence by principal of mathematical induction sum of first n terms of given series is n+n-1x+n-2x2+...+2xn-2+xn-1 Hope this information will clear your doubts about topic. Regards 0 View Full Answer Chharishma.r.nayaka answered this Plz answer soon...I hve math xam 2mrw..... 0
