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Mathematics
Mathematics
Problem
The value of
lim
n
→
∞
(
1
1
⋅
2
+
1
2
⋅
3
+
1
3
⋅
4
+
⋯
+
1
n
(
n
+
1
)
)
\lim_{n \to \infty} \left( \frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \frac{1}{3 \cdot 4} + \dots + \frac{1}{n(n+1)} \right)
lim
n
→
∞
(
1
⋅
2
1
+
2
⋅
3
1
+
3
⋅
4
1
+
⋯
+
n
(
n
+
1
)
1
)
is
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