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1996 Tournament Of Towns
(510) 3
TOT 510 1996 Autumn J A3 sum (k^2-2}/k! < 3
TOT 510 1996 Autumn J A3 sum (k^2-2}/k! < 3
Source:
August 16, 2024
algebra
inequalities
Problem Statement
Prove that
2
2
!
+
7
3
!
+
14
4
!
+
23
5
!
+
.
.
.
+
k
2
−
2
k
!
+
.
.
.
+
9998
100
!
<
3
\frac{2}{2!}+\frac{7}{3!}+\frac{14}{4!}+\frac{23}{5!}+...+\frac{k^2-2}{k!}+...+\frac{9998}{100!}<3
2
!
2
+
3
!
7
+
4
!
14
+
5
!
23
+
...
+
k
!
k
2
−
2
+
...
+
100
!
9998
<
3
where
n
!
=
1
×
2
×
.
.
.
×
n
.
n! = 1 \times 2 \times ... \times n.
n
!
=
1
×
2
×
...
×
n
.
(V Senderov)
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