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Question Number 94096 by Rio Michael last updated on 16/May/20

The result of adding the odd natural numbers is :

1 = 1

1 + 3 = 4

1 + 3 + 5 = 9

1 + 3 + 5 + 7 = 16

1 + 3 + 5 + 7 + 9 = 25

show that from this result, \underset{i = 1}{\sum^{n}} (2 i - 1) = n^{2} .

Commented by Kunal12588 last updated on 16/May/20

s u m o f A . P .

Answered by Kunal12588 last updated on 16/May/20

\underset{i = 1}{\sum^{n}} (2 i - 1) = 2 \underset{i = 1}{\sum^{n}} i - n = 2 \times \frac{n (n + 1)}{2} - n

= n^{2} + n - n = n^{2}

Commented by Rio Michael last updated on 16/May/20

perfect