C but i could be wrong lol very wrong.
3/4 cups of orange juice for 1 smoothie would be 3/4 x 2 = 2 smoothies.
3/4 (.75) x 2= 1 1/2 cups of orange juice.
You can make a start by putting together an expression for the sum of the even integers between 1 and k inclusive.
Let S be the sum of the even integers between 1 and k inclusive.
Then:
<span><span>S=2+4+6+⋯+(k−2)+k</span></span>
As k is even, you can say r = 2k and so:
<span><span>S=2(1+2+3+⋯+(r−1)+r)</span></span>
<span>Now the sum of the first </span><span>r</span><span> numbers is well-known, it's the </span><span>r</span>th triangle number and we have:
<span><span>1+2+3+⋯+(r−1)+r=<span><span>r(r+1)/</span>2</span></span></span>
<span>Now we can keep it simple and say </span><span><span>2k=4r </span></span><span>and so:</span>
<span><span>S=2(1+2+3+⋯+(r−1)+r)=4r=2<span><span>r(r+1)</span>2</span>=r(r+1)</span></span>
<span>So you can build a quadratic in </span><span>r</span><span> and so get </span><span>k.</span>
