Question 29

Fill in the blanks to make the statements true.

There are ___ natural numbers between $n^{2}$ and $(n + 1)^{2}$ .

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Solution

2n
Natural numbers between $n^{2}$ and $(n + 1)^{2} = [(n + 1)^{2} - n^{2}] - 1$
$= [n^{2} + 2 n + 1 - n^{2}] - 1 = 2 n + 1 - 1 = 2 n$

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