The question can be reduced to, what is the last digit of \(1 + 2^2 + 3^3 + 4^4 + 5^5 + 6^6\)

This is = 1 + 4 + 7 + 6 + 5 + 6 = 29. So the last digit is 9.


Option E

Arun Kumar
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Solution:

Recall that if the units digit of a positive integer n is d, and m is a positive integer, then both n^m and d^m have the same units digit. In other words, the given sum has the same units digit as:

1 + 2^2 + 3^3 + 4^4 + 5^5 + 6^6

2^2 = 4, 3^3 = 27, 4^4 = 256 and since any power of 5 has units digit of 5 and any power of 6 has units digit 6, the expression has the same units digit as:

1 + 4 + 7 + 6 + 5 + 6 = 29

Therefore, the units digit of the given sum is 9.

Answer: E
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