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Mathematics
Problem
If
f
(
x
)
=
lim
n
→
∞
(
1
+
x
)
(
1
+
x
2
)
(
1
+
x
2
2
)
(
1
+
x
2
3
)
…
(
1
+
x
2
n
)
f(x) = \lim_{n \to \infty} (1+x)(1+x^2)(1+x^{2^2})(1+x^{2^3})\dots(1+x^{2^n})
f
(
x
)
=
lim
n
→
∞
(
1
+
x
)
(
1
+
x
2
)
(
1
+
x
2
2
)
(
1
+
x
2
3
)
…
(
1
+
x
2
n
)
where
∣
x
∣
<
1
|x| < 1
∣
x
∣
<
1
, then - (A)
1
1
−
x
\frac{1}{1-x}
1
−
x
1
(B)
1
1
+
x
\frac{1}{1+x}
1
+
x
1
(C)
1
1
−
x
2
\frac{1}{1-x^2}
1
−
x
2
1
(D)
1
1
+
x
2
\frac{1}{1+x^2}
1
+
x
2
1
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