n-is-an-integer-prove-algebraically-that-the-sum-of-1-2-n-n-1-and-1-2-n-1-n-2-is-always-a-square-number-note-write-your-expression-in-a-form-that-clearly-shows-a-square-number-

Question Number 130257 by pete last updated on 23/Jan/21

n is an integer

prove algebraically that the sum of

\frac{1}{2} n (n + 1) and \frac{1}{2} (n + 1) (n + 2) is always

a square number .

note : w r i t e y o u r e x p r e s s i o n i n a f o r m

t h a t c l e a r l y s h o w s a s q u a r e n u m b e r .

Commented by Dwaipayan Shikari last updated on 23/Jan/21

\frac{1}{2} n (n + 1) + \frac{1}{2} (n + 1) (n + 2) = \frac{1}{2} (n + 1) (n + n + 2) = {(n + 1)}^{2}

Commented by pete last updated on 23/Jan/21

thank you sir, very much

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