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Shkiper50 [21]
3 years ago
7

N is an integer s=1/2 n(n+1) prove that 8s + 1 is an odd square number

Mathematics
1 answer:
pychu [463]3 years ago
7 0
s=\frac{1}{2}n(n+1) \\ \\
8s+1=8 \times \frac{1}{2}n(n+1)+1=4n(n+1)+1=4n^2+4n+1=(2n+1)^2

n is an integer, so 2n+1 is also an integer. 8s+1 is equal to the square of 2n+1, so it's a square number.

2n+1 is an odd integer for any value of n. The square of an odd integer is always an odd integer. Therefore 8s+1=(2n+1)² is odd.

8s+1 is an odd square number.
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