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\text { Last digit in } \sum_{k=1}^{999} k^m

Option: 1

0


Option: 2

1


Option: 3

2


Option: 4

3


Answers (1)

best_answer

You can add 1000^m to the sum as it will not change the last digit as its last digit is 0.Last digits of 1^m, 11^m, 21^m, \ldots, 991^m are the same. Similarly for 2^m, 12^m, \ldots, 992^m and so on till 10^m, 100^m, \ldots 1000^m. So the ones digit of 1^m+2^m+\ldots+10^m is the same as that of 11^m+12^m+\ldots+20^m and so on. There are 100 10 s in 1000 , so the ones digit of the sum is \left(1^m+2^m+\ldots+10^m\right) * 100 \quad \bmod 10 which is 0.

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Pankaj

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