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प्रश्न
The sum of successive odd numbers 1, 3, 5, 7, 9, 11, 13 and 15 is ______.
पर्याय
81
64
49
36
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उत्तर
The sum of successive odd numbers 1, 3, 5, 7, 9, 11, 13 and 15 is 64.
Explanation:
We know that, the sum of first n odd natural numbers is n2.
Given odd numbers are 1, 3, 5, 7, 9, 11, 13 and 15.
So, number of odd numbers, n = 8
The sum of given odd numbers = n2 = (8)2 = 64
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संबंधित प्रश्न
Find the square of the given number.
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From the pattern, we can say that the sum of the first n positive odd numbers is equal to the square of the n-th positive number. Putting that into formula:
1 + 3 + 5 + 7 + ... n = n2, where the left hand side consists of n terms.
Observe the following pattern \[1^2 = \frac{1}{6}\left[ 1 \times \left( 1 + 1 \right) \times \left( 2 \times 1 + 1 \right) \right]\]
\[ 1^2 + 2^2 = \frac{1}{6}\left[ 2 \times \left( 2 + 1 \right) \times \left( 2 \times 2 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 = \frac{1}{6}\left[ 3 \times \left( 3 + 1 \right) \times \left( 2 \times 3 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 + 4^2 = \frac{1}{6}\left[ 4 \times \left( 4 + 1 \right) \times \left( 2 \times 4 + 1 \right) \right]\] and find the values :
12 + 22 + 32 + 42 + ... + 102
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