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Question

limx3nr1xrnr13rx3 is equal to 



Your Answer
A

(2n1)×3n4

 

Correct Answer
B

(2n1)×3n+14

Your Answer
C

(2n1)3n+1

Your Answer
D

(2n1)×3n+14


Solution

The correct option is B

(2n1)×3n+14


limx3nr1xrnr13rx3
=limx3x1+x2+x3++xn(31+32+333n)x3
=limx3x3x3+x232x3+x333x3+xn3nx3
=1+2×3+3×32++n3n1
[xnanxa=nan1]
This series is an AGP of the form given below:
S=1+2r+3r2mn1
S=1rn(1r)2nrn1r
r=3,a=1,d=1
=13n+2n3n4
=3n(2n1)+14
 

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