Why does nnn…=n

Advadlippabrj

Advadlippabrj

Answered

2022-01-24

Why does
nnn=n

Answer & Explanation

Jason Duke

Jason Duke

Expert

2022-01-25Added 11 answers

X=nnn
=nnn
=n12n14n18
=n12+14+18
=n1
=n
SaphypycleDapc5

SaphypycleDapc5

Expert

2022-01-26Added 11 answers

Suppose y=xxx
Multiply both sides by x and take the square root:
xy=xxx...=y
Therefore, xy=y, and solving we have xy=y2x=y

RizerMix

RizerMix

Expert

2022-01-27Added 437 answers

It is important to show that the limit exists. Let define the sequence ak=nak1 Since akak1=nak1 and akn=ak1n, we have 1. if ak1n, then ak1akn; that is, ak is increasing and bounded above by n. 2. if ak1n, then ak1akn; that is, ak is decreasing and bounded below by n. In either case, ak is convergent. Using the continuity of multiplication by a constant and the continuity of square root, we get limkak=limknak1=nlimkak Squaring and dividing by limkak, we get that limkak=n

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