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WechatIMG199.jpegRecursively define numbers an for n∈N by a1:=5 and

an+1:=1+an for n≥1.Then

a2 = 1+5 = 2, a3 = 1+2 = 1, a4 = 1+1 = 2 , etc. Show3333

1 < an+1 < an2

WechatIMG199.jpeg

1. Recursively define numbers an for n E N by a1 := 5 and an+1 := Itan for n &gt; 1. Then
a2 = 145 = 2, a3 = 3
1+2 = 1, a4 = 14 = 2, etc. Show
&lt; an+1 &lt; an
for each n E N.

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New Doc 2019-10-03 14.08.41_2.jpg

anti = It an
3
As an 7 2
So antif
1+ 72
3
W /N / W
So anti 7 /2
Now
anti = 1+ as
3
So anti - an as
it as and an 7 0
So to
of an is less than An
anti = it an
3
3 anti = 1 7 an
or an = 3 anti- 1
so...

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