prove that the difference between the squares of two consecutive natural number is equal to their sum.
prove that the difference between the squares of two consecutive natural number is equal to their sum.
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Verified answer
Let the two consecutive natural numbers be x and x+1Difference between the squares of two consecutive natural numbers is:-
(x)²-(x+1)²
=x²-[x²+1¹+2(x)(1)]
=x²-(x²+1+2x)
=x²-x²+1+2x
=2x+1
The sum of consecutive natural numbers is;-
x+(x+1)
=x+x+1
=2x+1
Both are equal. Hence proved
For example,
Let the two consecutive natural numbers be 2 and 3
Difference between the squares of those numbers is:-
(3)²-(2)²
=9-4
=5
Sum of those consecutive natural numbers is:-
2+3
=5
So proved.
Hope it helps