find the sum of all the first n odd natural number
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The first n odd natural numbers are given by 1,3,5,7,9…… (2n – 1) and this forms an AP.
a = 1
d = 2
tn = (2n – 1)
The formula of sum of an A.P series
S = n/2[2a + (n − 1) × d]
S = n /2 [2 + 2n – 2]
S = n /2 [2n]
S = n2
The sum of first n odd natural numbers is n2.
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n2
- Natural numbers are part of the number system that comprises all the positive integers from 1 to infinity and are often used for the purpose of counting.
- Zero not include in natural numbers. In reality, 1,2,3,4,5,6,7,8,9…. are known as counting numbers.
- Natural numbers are real numbers, which only contain positive integers, i.e. 1, 2, 3, 4,5,6, ………. With zero, fractions, decimals, and negative numbers excluded.
- The first n odd natural numbers are given by 1,3,5,7,9…… (2n – 1) and this forms an AP.
a = 1
d = 2
tn = (2n – 1)
The formula of sum of an A.P series
S = n/2[2a + (n − 1) × d]
S = n /2 [2 + 2n – 2]
S = n /2 [2n]
S = n2
The sum of first n odd natural numbers is n2.
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