Question

Check whether 2" can end with the digit 6 for any nɛ N.​

Answer 1

Step-by-step explanation:

yes because 6 is divisible by 2so it can end with 6 for example 2^4 = 16

Answer 2

Step-by-step explanation:

Yes, $2^n$ can end with the digit 6 for some certain n ∈ N , not for all n .

For this let's check the pattern of the last digit given by $2^n$.

$2^1$ = 2 , this ends with 2

2² = 4 , this ends with 4 .

2³ = 8 , this ends with 8 .

$2^4$ = 16 , THIS ENDS WITH A 6 .

$2^5$ = 32 , this ends with a 2 and so on .

So the pattern of the last digits is like 2,4,8,6,2,4,8,6....  and so on .

Notice that, when n is a multiple of 4 , $2^n$ ends with a 6 .

So if n = 4k , where k ∈ N , then $2^n$ ends with a 6 .

Hope this helps you.

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