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· seq-3
Sequences & Series · Telescoping
AIME style
●●●●○ 7/10
~5 min
⏱ 0:00
Let
S
=
∑
k
=
1
99
1
k
(
k
+
1
)
S = \sum_{k=1}^{99} \tfrac{1}{k(k+1)}
S
=
∑
k
=
1
99
k
(
k
+
1
)
1
. If
S
=
m
n
S = \tfrac{m}{n}
S
=
n
m
in lowest terms, what is
m
+
n
m + n
m
+
n
?
telescoping
partial-fractions
Submit
Hint 1 of 3
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