We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
105
1
avatar+817 

please explain thanks

 Nov 27, 2018
 #1
avatar+99415 
+2

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

17 Online Users

avatar
avatar
avatar