Let `U_1=1,\ U_2=1\ a n d\ U_(n+2)=U_(n+1)+U_nfor\ ngeq1.` use mathematical induction to show that: `U_n=1/(sqrt(5)){((1+sqrt(5))/2)^n-\ ((1-sqrt(5))/2)^n}\ for\ a l l\ ngeq1.`

Explanation

We have to prove
`U_n=1/(sqrt(5)){((1+sqrt(5))/2)^n-\ ((1-sqrt(5))/2)^n}\ for\ a l l\ ngeq1.`



`U_1=1/(sqrt(5)){((1+sqrt(5))/2)^1-\ ((1-sqrt(5))/2)^1}\ for\ a l l\ ngeq1.`



`U_2=1/(sqrt(5)){((1+sqrt(5))/2)^2-\ ((1-sqrt(5))/2)^2}\ for\ a l l\ ngeq1.`



Hence (1) holds for n = 1 and n = 2
Now assume
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