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NDA Math Sequences and Series
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© examsnet.com
Question : 58
Total: 79
What is the greatest value of the positive integer n satisfying the condition
1
+
1
2
+
1
4
+
1
8
+
.
.
.
+
1
2
n
−
1
<
2
−
1
1000
?
[NDA II 2016]
8
9
10
11
Validate
Solution:
1
+
1
2
+
1
4
+
1
8
+
.
.
.
.
.
.
.
.
.
+
1
2
n
−
1
<
2
−
1
1000
LHS of given inequality is in GP.
∴
1
−
1
2
n
1
−
1
2
<
2
−
1
1000
⇒
2
−
1
2
n
−
1
<
2
−
1
100
⇒
2
n
−
1
<
1000
Now,
(
2
)
9
=
512
&
(
2
)
10
=
1024
∴
n
−
1
=
9
⇒
n
=
10
© examsnet.com
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