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1 + 2 + 3 + 4 +...=100 + 98 + 96 + 94 +... - 2016 Ecuador Juniors (OMEC) L2 p4
1 + 2 + 3 + 4 +...=100 + 98 + 96 + 94 +... - 2016 Ecuador Juniors (OMEC) L2 p4
Source:
October 24, 2022
algebra
Problem Statement
Two sums, each consisting of
n
n
n
addends , are shown below:
S
=
1
+
2
+
3
+
4
+
.
.
.
S = 1 + 2 + 3 + 4 + ...
S
=
1
+
2
+
3
+
4
+
...
T
=
100
+
98
+
96
+
94
+
.
.
.
T = 100 + 98 + 96 + 94 +...
T
=
100
+
98
+
96
+
94
+
...
. For what value of
n
n
n
is it true that
S
=
T
S = T
S
=
T
?
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