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AIEEE 2002 Math Solved Paper
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© examsnet.com
Question : 20
Total: 74
If
a
n
=
√
7
+
√
7
+
√
7
+
.
.
.
.
.
.
.
.
.
having
n
radical signs then by methods of mathematical induction which is true
a
n
>
7
∀
n
≥
1
a
n
<
7
∀
n
≥
1
a
n
<
4
∀
n
≥
1
a
n
>
3
∀
n
≥
1
Validate
Solution:
Given
a
n
=
√
7
+
√
7
+
√
7
+
.
.
.
.
.
.
.
.
.
∴
a
n
=
√
7
+
a
n
⇒
a
n
2
=
7
+
a
n
⇒
a
n
2
−
a
n
−
7
=
0
⇒
a
n
=
1
±
√
1
−
4
×
1
×
−
7
2
⇒
a
n
=
1
±
√
29
2
As
a
n
>
0
∴
a
n
=
1
+
√
29
2
=
3.19
So
a
n
>
3
∀
n
≥
1
© examsnet.com
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