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I have no idea what to do here:

 

The sequence (u_n) is defined by u_0 = 0 and \(u_n = \dfrac{1}{2 + u_{n - 1}}\)

 

Compute u_5.

 Jun 2, 2020
 #1
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u0  =  0

 

un  =  1 / ( 2 + un-1 )

 

We'll have to work our way up from u0 to u5.

 

u1  =  1 / ( 2 + u0 )     --->     u1  =  1 / ( 2 + 0 )  =  1/2

 

u2  =  1 / ( 2 + u1 )     --->     u2  =  1 / ( 2 + 1/2 )  =  2/5

 

u3  =  1 / ( 2 + u2 )     --->     u3  =  1 / ( 2 + 2/5 )  =  5/12

 

u4  =  1 / ( 2 + u3 )     --->     u4  =  1 / ( 2 + 5/12 )  =  12/29

 

u5  =  1 / ( 2 + u4 )     --->     u5  =  1 / ( 2 + 12/29 )  =  ............. 

 Jun 2, 2020

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