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1991 Nordic
3
prove that 1/2^2 +1/3^2 +...+1/n^2 <2/3
prove that 1/2^2 +1/3^2 +...+1/n^2 <2/3
Source: Nordic Mathematical Contest 1991 #3
October 5, 2017
induction
inequalities
positive integer
Problem Statement
Show that
1
2
2
+
1
3
2
+
.
.
.
+
1
n
2
<
2
3
\frac{1}{2^2} +\frac{1}{3^2} +...+\frac{1}{n^2} <\frac{2}{3}
2
2
1
+
3
2
1
+
...
+
n
2
1
<
3
2
for all
n
≥
2
n \ge 2
n
≥
2
.
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