Question by Summer Clouds - Discuss with MathYouLike

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25/09/2017 at 17:28

Find the last-digit of sum \(A=5+5^2+....+5^{100}\).

List of answers

Lê Quốc Trần Anh Coordinator 25/09/2017 at 18:13

We have: \(5^n=...5\)

=> \(A=...5+...5+...+...5\left(100-factors\right)\)

We have: \(...5\left(2n-factors\right)=...0\)

=> \(A=...0\)

So the last digit of A is: 0
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Vũ Trung Dũng 27/09/2017 at 18:48

We have: 5x = ...5 with $\forall x \in$ N*

=> A = ...5 + ...5 + ... + ...5

And the number of terms of A are:

100 - 1 + 1 = 100 [terms]

So last-digit of A is: ...5 * 100 = ...500 = ...0

So, the answer is 0
Dao Trong Luan 25/09/2017 at 18:05

We have: 5^x = ...5 with \(\forall x\in\) N*

=> A = ...5 + ...5 + ... + ...5

And the number of terms of A are:

100 - 1 + 1 = 100 [terms]

So last-digit of A is: ...5 * 100 = ...500 = ...0

So, the answer is 0

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