Solve the following:::  please try to give a detailed answer and no Links

lim x 3 r = 1 n X r - r = 1 n 3 r x - 3


 

Dear student
limx3r=1nxr-r=1n3rx-3=limx3x1+x2+...xn-31+32+...+3nx-3=limx3x-3x-3+x2-32x-3+x3-33x-3+...+xn-3nx-3=1+2×3+3×32+...+n3n-1    xn-anx-a=nan-1This series in an AGP of the form given below:S=1+2r+3r2+...nrn-1=1-rn1-r2-nrn1-rr=3,a=1 ,d=1=1-3n+2n×3n4=3n2n-1+14
Regards

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