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Question
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
1112 − 1092
Solution
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`
1112 − 1092 = 1112 − 1102 + 1102 − 1092
= (111 + 110) + (110 + 109)
= 440
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