the sum of first n odd positive integers is
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Answer:
the sum of first n positive integers is n(n+1)/2
Answered by
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The sequence of the first n odd positive integer numbers is 1,3,5,7,9,...,2n−1.
a
1
=1,d=2
We know that S
n
=a
1
+a
2
+a
3
+....a
n
=
2
n
[2a
1
+(n−1)d]
S
n
=
2
2n−1
[(2×1+2n−1−1)×2]
S
n
=
2
2n−1
[(2n)×2]
S
n
=2n(2n−1)
S
n
=4n
2
a
1
=1,d=2
We know that S
n
=a
1
+a
2
+a
3
+....a
n
=
2
n
[2a
1
+(n−1)d]
S
n
=
2
2n−1
[(2×1+2n−1−1)×2]
S
n
=
2
2n−1
[(2n)×2]
S
n
=2n(2n−1)
S
n
=4n
2
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