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Mathematics
Mathematics
Problem
The geometric series
∑
k
=
0
∞
5
(
1
4
)
k
\displaystyle \sum_{k=0}^{\infty} 5\left(\tfrac14\right)^k
k
=
0
∑
∞
5
(
4
1
)
k
converges to
S
=
20
3
S=\dfrac{20}{3}
S
=
3
20
. Determine the least integer
N
N
N
such that
∣
S
−
S
N
∣
<
0.01
|S-S_N|<0.01
∣
S
−
S
N
∣
<
0.01
.
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