Find the sum of first n odd natural numbers.
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Hence this series is an Arithmetic Progression. First term of this sequence is 1 and the common difference is 2. So we get our sequence is arithmetic progression with a = 1 and d = 2. Hence the sum of the first n odd natural number is n2.
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Find the sum of first n odd natural numbers.
❇ Solution ⬇
The sequence of first n odd numbers is
1,3,5,7.........n
This forms an A.P with a=1 and d=2
S = n/2{2a+(n−1)d}
⇒S = n/2{2(1)+(n−1)2}
⇒S = n/2(2n)
⇒S = n²
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