quote:

**Neather2 wrote**:

**2)**

What is the sum of the first 2450 natural integers **numbers?**

Sums of natural integers and their numbers are different.

Sum of integers from 10 to 15 is 10+11+12+13+14+15=75

Sum of integers' numbers from 10 to 15 is 1+0+1+1+1+2+1+3+1+4+1+5=21

I thought you were asking for the latter. The answer I gave you is correct, it's just for the wrong problem.

EDIT: Regarding triangles.

Lines that make up the red triangle are 3 and 8 squares long. It's hypotenuse is sqrt(73) or approx. 8.554. The sine of the smallest angle is 3/sqrt(73) = 0.351123, which gives us angle's size - 20.556 degrees.

If we do the same thing for the green triangle, the respectable sine is 0.371391, and angle's size is 21.801 degrees.

These angles mismatch. This means, that the figures are not triangles in the first place: the "

hypotenuse"

in the top figure is shaped inwards, while the bottom one it is shaped outwards, accomodating the extra square.

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*[Last edited by eb0ny at 02-06-2009 10:01 AM]*