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UPSC CDS Math Square, Roots and Surds Questions
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© examsnet.com
Question : 10
Total: 22
The value of
√
1
+
√
1
+
√
1
+
.
.
.
[2017 CDS-II]
Equals to 1
Lies between 0 and 1
Lies between 1 and 2
Is greater than 2
Validate
Solution:
Let
x
=
√
1
+
√
1
+
√
1
+
.
.
.
⇒
x
=
√
1
+
x
⇒
x
2
−
x
−
1
=
0
⇒
x
=
1
±
√
5
2
But, x cannot be negative.
∴
x
=
1
+
√
5
2
=
1.62
(Approx)
⇒ 1 < x < 23
© examsnet.com
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