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प्रश्न
There are ______ natural numbers between n2 and (n + 1)2
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उत्तर
There are 2n natural numbers between n2 and (n + 1)2
Explanation:
Natural number between n2 and (n + 1)2 will be calculated as follows:
= [(n + 1)2 – n2] – 1
= (n2 + 2n + 1 – n2) – 1
= 2n + 1 – 1
= 2n
Hence, there are 2n natural numbers between n2 and (n + 1)2.
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संबंधित प्रश्न
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\[ 1 + 2 + 3 = \frac{1}{2}\left\{ 3 \times \left( 3 + 1 \right) \right\}\]
\[1 + 2 + 3 + 4 = \frac{1}{2}\left\{ 4 \times \left( 4 + 1 \right) \right\}\]and find the values of following:
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\[ 1^2 + 2^2 = \frac{1}{6}\left[ 2 \times \left( 2 + 1 \right) \times \left( 2 \times 2 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 = \frac{1}{6}\left[ 3 \times \left( 3 + 1 \right) \times \left( 2 \times 3 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 + 4^2 = \frac{1}{6}\left[ 4 \times \left( 4 + 1 \right) \times \left( 2 \times 4 + 1 \right) \right]\] and find the values :
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