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प्रश्न
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
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उत्तर
From the pattern, we can say that the difference between the squares of two consecutive numbers is the sum of the numbers itself.
In a formula:
`(n+1)^2-(n)2=(n+1)+n`
Using this formula, we get:
(i) 1002 − 992 = (99 + 1) + 99
= 199
संबंधित प्रश्न
Find the square of the given number.
32
Find the square of the given number.
71
What will be the units digit of the square of the following number?
52
What will be the units digit of the square of the following number?
12796
Which of the following triplet pythagorean?
(14, 48, 51)
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 :
52 + 62 + 72 + 82 + 92 + 102 + 112 + 122
Find the squares of the following numbers using diagonal method:
273
Find the square of the following number:
205
Find the square of the following number:
995
The sum of first n odd natural numbers is ______.
