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Question

limn1+a+a2+...+an11+b+b2+...+bn1=0 if:

A
a=b
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B
a<b
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C
a>b
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D
a>1
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Solution

The correct options are
B a<b
D a>1
limn1+a+a2+...+an11+b+b2+...+bn1

=limn1an1a11bn1b1=limnb1a1an1bn1form
L Hospital
=limn(b1a1)anlogabnlogb=(b1)loga(a1)logblimn(ab)n

limn(ab)n=0 if ab<1
a<b
& a>1
because limn(an1)(bn1)=
if a<1
limnan=(1P)n(P>1)
=1P=1=0

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