Evaluate this expression: 15C4
1 answer:
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First you need to find the slope of the line containing those 2 points using the slope formula. Filling in with our info we have 
. So the slope is -1.5. Now we need to find out the rest of the info, mainly the y-intercept. The line appears to go through the y axis at (0, 0), but let's make sure. We will use the slope we just found and one of our points to solve for the y-intercept. I picked point (4, -6). Filling in to solve for b we get -6 = (-1.5)(4) + b. Doing the multiplication on the right gives us -6=-6 + b. Add 6 to both sides to get that b = 0. Now let's use that and the slope we found to rewrite the equation in slope-intercept form. y = -1.5x + 0 or y = -1.5x and there you go!
a. Notice that
1/(1*2) = 1/2 = 1 - 1/2
1/(2*3) = 1/6 = 1/2 - 1/3
1/(3*4) = 1/12 = 1/3 - 1/4
and so on, which suggests the n-th term of the sum can be written as
Then the sum itself is telescoping:
b. The proof is trivial:
so the formula found in (a) is correct.