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If the sum 1+2+3+4...k is a perfect square N^2 and if N is smaller than 300 then number of values of K

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Pls solve this it's urgent

highway shekhar - 2 years, 10 months ago

So the number is a triangular perfect square. 36 is one example

Mohammad Farhat - 2 years, 10 months ago

36 is the only triangular perfect square lesser than a 300

Mohammad Farhat - 2 years, 10 months ago

I tested all the triangular numbers until the sum exceeded 300

Mohammad Farhat - 2 years, 10 months ago

Triangular numbers can be attained using $\frac{n times (n+1)}{2}$

Mohammad Farhat - 2 years, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$