Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges. startfraction 7 over 2 times 3 endfraction plus startfraction 7 over 3 times 4 endfraction plus startfraction 7 over 4 times 5 endfraction plus midline ellipsis plus startfraction 7 over (n plus 1 )(n plus 2 )endfraction plus midline ellipsis 7 2•3+ 7 3•4+ 7 4•5+⋯+ 7 (n+1)(n+2)+⋯ what is the formula for the nth partial sum of the series?

10 glasses of juice could be made with 5 carrots, 1,500 orange juice, 2,000 papaya juice.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

graph them on a graphing calculator, press 2nd trace. select intersect. hit enter until it says answer. ti 84 works best

step-by-step explanation: