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Mathematics
Mathematics
Problem
Examine the continuity at
x
=
0
x = 0
x
=
0
of the sum function of the infinite series
x
x
+
1
+
x
(
x
+
1
)
(
2
x
+
1
)
+
x
(
2
x
+
1
)
(
3
x
+
1
)
+
…
\frac{x}{x+1} + \frac{x}{(x+1)(2x+1)} + \frac{x}{(2x+1)(3x+1)} + \dots
x
+
1
x
+
(
x
+
1
)
(
2
x
+
1
)
x
+
(
2
x
+
1
)
(
3
x
+
1
)
x
+
…
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