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Mathematics
Mathematics
Problem
Find the sum of the series
∑
r
=
0
n
(
−
1
)
r
n
C
r
{
1
2
r
+
3
r
2
2
r
+
7
r
2
3
r
+
15
r
2
4
r
+
…
upto
m
terms
}
.
\sum_{r=0}^{n} (-1)^r {}^n C_r \left\{ \frac{1}{2^r} + \frac{3^r}{2^{2r}} + \frac{7^r}{2^{3r}} + \frac{15^r}{2^{4r}} + \dots \text{upto } m \text{ terms} \right\}.
r
=
0
∑
n
(
−
1
)
r
n
C
r
{
2
r
1
+
2
2
r
3
r
+
2
3
r
7
r
+
2
4
r
1
5
r
+
…
upto
m
terms
}
.
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