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National and Regional Contests
Albania Contests
Albania JBMO TST
2015 Albania JBMO TST
1
1
Part of
2015 Albania JBMO TST
Problems
(1)
Compute the sum $a_1+a_2+\ldots+a_{2015}.$
Source: Albania JTST 2015
10/4/2023
For every positive integer
n
n{}
n
denote
a
n
a_n
a
n
as the last digit of the sum of the number from
1
1
1
to
n
n{}
n
. For example
a
5
=
5
,
a
6
=
1.
a_5=5, a_6=1.
a
5
=
5
,
a
6
=
1.
a) Find
a
21
.
a_{21}.
a
21
.
b) Compute the sum
a
1
+
a
2
+
…
+
a
2015
.
a_1+a_2+\ldots+a_{2015}.
a
1
+
a
2
+
…
+
a
2015
.