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Mathematics
Mathematics
Problem
The sum of the series
2
1
⋅
2
+
5
2
⋅
3
2
1
+
10
3
⋅
4
2
2
+
17
4
⋅
5
2
3
+
…
\frac{2}{1 \cdot 2} + \frac{5}{2 \cdot 3} 2^1 + \frac{10}{3 \cdot 4} 2^2 + \frac{17}{4 \cdot 5} 2^3 + \dots
1
⋅
2
2
+
2
⋅
3
5
2
1
+
3
⋅
4
10
2
2
+
4
⋅
5
17
2
3
+
…
upto
n
n
n
terms is equal : (a)
n
2
n
n
+
1
\frac{n2^n}{n+1}
n
+
1
n
2
n
(b)
(
n
n
+
1
)
2
n
+
1
\left(\frac{n}{n+1}\right) 2^n + 1
(
n
+
1
n
)
2
n
+
1
(c)
n
2
n
n
+
1
−
1
\frac{n2^n}{n+1} - 1
n
+
1
n
2
n
−
1
(d)
(
n
−
1
)
2
n
n
+
1
\frac{(n-1)2^n}{n+1}
n
+
1
(
n
−
1
)
2
n
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