ONE
All Portugal
Númas
EN
Sign in
← Back to the programme
Olympiad
Easy
Number Theory
7–9
What is the remainder when
1
+
2
+
3
+
⋯
+
100
1 + 2 + 3 + \cdots + 100
1
+
2
+
3
+
⋯
+
100
is divided by
7
7
7
?
Qual é o resto da divisão de
1
+
2
+
3
+
⋯
+
100
1 + 2 + 3 + \cdots + 100
1
+
2
+
3
+
⋯
+
100
por
7
7
7
?
Answer options
A.
4
B.
3
C.
0
D.
5
Check Answer
Solution
Step 1 of 3
1.
Pair the terms as Gauss did: the sum is
100
×
101
2
=
5050
\frac{100 \times 101}{2} = 5050
2
100
×
101
=
5050
.
Next step
Show full solution