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please explain thanks

 Nov 27, 2018
 #1
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un = 3 * 2n-1 - 1     

Prove this is true for  n = 1

u1 = 3 * 2 1 - 1 + 1

u1 = 3 * 1 - 1 =   2     which is true

 

Asume that it is true for n = k

That is : 

uk = 3 * 2k-1 - 1

 

Show that it is true for n = k + 1

 

uk+1 = 3 * 2 (k + 1 - 1)  - 1

 

uk+1 = 3 * 2k - 1     (1)

 

And we were given  that

 

uk+1  = 2uk + 1        (2)

 

So....by our assumption uk = 3 * 2k-1 - 1    (3)

 

Sub    (3) into (2)

 

uk+1  = 2 ( 3 * 2k-1 - 1) + 1  =

 

2 * 3 * 2k-1 - 2 + 1  =

 

3 * 2 * 2k-1 - 1 =

 

3 * ( 21 * 2k-1) - 1 =

 

3 * ( 2 k - 1 + 1)  - 1   = 

 

3 * 2k - 1        which   equals  ( 1)

 

 

cool cool cool

 Nov 27, 2018

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