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Mathematics
Problem
Let
T
=
∑
k
=
1
∞
(
−
1
)
k
+
1
1
2
k
−
1
T=\sum_{k=1}^{\infty} (-1)^{k+1}\frac{1}{2k-1}
T
=
∑
k
=
1
∞
(
−
1
)
k
+
1
2
k
−
1
1
. Compute the sum of the first six terms and state an interval of length less than
0.1
0.1
0.1
that must contain the exact value of
T
T
T
.
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