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Mathematics
Mathematics
Problem
Let
0
<
t
<
1
0<t<1
0
<
t
<
1
. Consider the two series
A
=
∑
n
=
0
∞
t
n
A = \displaystyle \sum_{n=0}^{\infty} t^{n}
A
=
n
=
0
∑
∞
t
n
and
B
=
∑
n
=
0
∞
(
0.5
)
n
.
B = \displaystyle \sum_{n=0}^{\infty} \left(0.5\right)^{n}.
B
=
n
=
0
∑
∞
(
0.5
)
n
.
Determine all values of
t
t
t
for which the sum of series
A
A
A
is greater than the sum of series
B
B
B
.
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