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Mathematics
Mathematics
Problem
If
0
<
x
<
1
0 < x < 1
0
<
x
<
1
, then
3
2
x
2
+
5
3
x
3
+
7
4
x
4
+
…
\frac{3}{2}x^2 + \frac{5}{3}x^3 + \frac{7}{4}x^4 + \dots
2
3
x
2
+
3
5
x
3
+
4
7
x
4
+
…
, is equal to (a)
x
(
1
−
x
1
+
x
)
+
log
e
(
1
−
x
)
x \left( \frac{1-x}{1+x} \right) + \log_e(1-x)
x
(
1
+
x
1
−
x
)
+
lo
g
e
(
1
−
x
)
(b)
x
(
1
+
x
1
−
x
)
+
log
e
(
1
−
x
)
x \left( \frac{1+x}{1-x} \right) + \log_e(1-x)
x
(
1
−
x
1
+
x
)
+
lo
g
e
(
1
−
x
)
(c)
1
+
x
1
−
x
+
log
e
(
1
−
x
)
\frac{1+x}{1-x} + \log_e(1-x)
1
−
x
1
+
x
+
lo
g
e
(
1
−
x
)
(d)
1
−
x
1
+
x
+
log
e
(
1
−
x
)
\frac{1-x}{1+x} + \log_e(1-x)
1
+
x
1
−
x
+
lo
g
e
(
1
−
x
)
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