Question

2^2^n+1 has unit digit 7 for all n>=2,n is Integer.Plz solve it fast by induction.

Answer 1

9

It can be proved with one more condition that ‘n’ is even.

Consider (2^(2 ^n)) +1

We have the formula((a) ^m)^n= (a) ^mn

(2^(2 ^n)) +1

= (2^2)^n)+1

=(4)^n + 1

Now observe that for any n=1,2,3…

= (4)^n ends either with 4 or 6

Ex: (4)^2=16 ends with 6

(4)^3=64 ends with 4

(4)^4=256 ends with 6

Also observe that whenever n is even,

(4)^n ends with 6

So that (4)^n +1 ends with 7 or will have 7ay the unit place.

Answer 2

hope this helps you....