First slide
Introduction to P.M.I

If un+1=3un2un1 and u0=2,u1=3 then un s equal to



step I : Given u1=3=2+1=21+1 which is true for n =1 , 

Put n =1in Eq. (i), 


which is true for n =2. Therefore, the result are true for n = 1 and n = 2

step II : Assume it is true for n = &, then it is also true for n =k-1.


Step lll : On putting n = k in Eq. (i), we get

         uk+1=3uk2uk1=32k+122k1+1 [from Eqs. (ii) and (iii)] =32k+322k12=32k+32k2=(31)2k+1=22k+1=2k+1+1

This shows that the result is true for n =k + 1, hence by the principle of mathematical induction the result is true for all nN

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