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UPSC NDA Math Model Paper 1
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© examsnet.com
Question : 14
Total: 120
What is the mean of first n natural numbers ?
n
(
n
+
1
)
2
n
(
n
+
1
)
2
None of the above
Validate
Solution:
Concept:
Suppose there are 'n' observations
{
x
1
,
x
2
,
x
3
,
.
.
.
,
x
n
}
Mean
(
x
)
=
(
x
1
+
x
2
+
x
3
+
.
.
.
+
x
n
)
n
=
n
∑
i
=
1
x
i
n
Sum of the natural numbers
=
n
(
n
+
1
)
2
Calculation:
To find: Mean of first n natural numbers
As we know, Sum of first n natural numbers
=
n
(
n
+
1
)
2
Now, Mean
=
n
(
n
+
1
)
2
n
=
(
n
+
1
)
2
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