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प्रश्न
The sum of first n odd natural numbers is ______.
विकल्प
2n + 1
n2
n2 – 1
n2 + 1
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उत्तर
The sum of first n odd natural numbers is n2.
Explanation:
Sum of first n odd natural numbers
= `sum(2n - 1) = 2sumn - n`
= `(2 xx n(n + 1))/2 - n`
= n(n + 1) – n
= n2 + n – n
= n2
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संबंधित प्रश्न
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
22 − 12 = 2 + 1
32 − 22 = 3 + 2
42 − 32 = 4 + 3
52 − 42 = 5 + 4
and find the value of
1002 − 992
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
Which of the following number square of even number?
225
Which of the following number is squares of even number ?
256
Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication:
37
Find the squares of the following numbers using diagonal method:
348
Find the square of the following number:
95
If m is the square of a natural number n, then n is ______.
Find the length of the side of a square if the length of its diagonal is 10 cm.
