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NDA Math Sequences and Series
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© examsnet.com
Question : 57
Total: 79
The sum of the first n terms of the series
1
2
+
3
4
+
7
8
+
15
16
+
.
.
.
is equal to
[NDA I 2017]
2
n
−
n
−
1
1
−
2
−
n
2
−
n
+
n
−
1
2
n
−
1
Validate
Solution:
1
2
+
3
4
+
7
8
+
15
16
+
.
.
.
=
(
1
−
1
2
)
+
(
1
−
1
4
)
+
(
1
−
1
8
)
+
.
.
.
.
.
=
n
−
(
1
2
+
1
4
+
1
8
+
.
.
.
.
.
)
=
n
−
1
2
(
1
−
1
2
n
)
1
2
=
n
−
1
+
2
−
n
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