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UPSC NDA Math Model Paper 8
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© examsnet.com
Question : 49
Total: 120
What is the value of
1
+
i
2
+
i
4
+
i
6
+
.
.
.
.
+
i
100
where
i
=
√
1
?
0
1
-1
None of the above
Validate
Solution:
Consider
1
+
i
2
+
i
4
+
i
6
+
.
.
.
.
+
i
100
Here,
i
=
√
1
⇒
i
2
=
−
1
Series becomes,
⇒ 1 - 1 + 1 - 1 + .... + 1
which is GP with common ratio r = -1 and first term a = 1.
⇒
1
−
1
+
1
−
1
+
.
.
.
.
.
+
1
=
a
(
1
−
r
n
)
1
−
r
Here
n
=
51
⇒
1
−
1
+
1
−
1
+
.
.
.
.
.
+
1
=
1
[
1
−
(
−
1
)
51
]
1
−
(
−
1
)
⇒
1
−
1
+
1
−
1
+
.
.
.
.
.
+
1
=
1
Hence,
1
+
i
2
+
i
4
+
i
6
+
.
.
.
.
.
+
i
100
=
1
© examsnet.com
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