Question

1 power 11+2 power 11 + 2 power 11+ 3 power 11 + 4 power 11 is divisible by 5

Answer 1

Answer:

Yes, the resultant is divisible by 5

Step-by-step explanation:

This type of problem can be solved by computing the one's digits of the respective powers.

1¹¹ = one's digit will be 1

2¹¹ = one's digit will be 8

3¹¹ = one's digit will be 7

4¹¹ = one's digit will be 4

since excluding these one's digit, the rest of the number will always be divisible by 5, hence the sum of these powers will be equivalent to a multiple of 5 and the summation of these one's digit.

1¹¹ + 2¹¹ + 3¹¹ + 4¹¹ = 5n + 1 + 8 + 7 + 4

= 5n + 20

= 5( n + 4)

Hence the sum of these powers will be divisible by 5.