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Mathematics
Mathematics
Problem
Evaluate these geometric series: a.
∑
k
=
1
10
3
×
2
k
−
1
\sum_{k=1}^{10} 3 \times 2^{k-1}
∑
k
=
1
10
3
×
2
k
−
1
b.
∑
k
=
1
12
(
1
2
)
k
−
2
\sum_{k=1}^{12} \left(\frac{1}{2}\right)^{k-2}
∑
k
=
1
12
(
2
1
)
k
−
2
c.
∑
k
=
1
25
6
×
(
−
2
)
k
\sum_{k=1}^{25} 6 \times (-2)^k
∑
k
=
1
25
6
×
(
−
2
)
k
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