Consider the series ∑n=0[infinity](34)n. The first four terms in the sequence of partial sums for this series are 1, 3/4, 9/16, 27/64 . Enter a comma separated list of numbers (in order). The nth partial sum is Sn=1+3/4+(3/4)2+(3/4)3+⋯+(3/4)n= . Enter a closed-form expression for this sum. The sum of this geometric series is ∑n=0[infinity](34)n=limn→[infinity] (

2160ft3

step-by-step explanation:

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

the 8 in 8,420 is in the thousands place so it's value is 8 thousand.

the 8 in 6,870 is in the hundreds place so it's value is 8 hundred.

divide 8000 by 800 to find the answer:

8000 / 800 = 10

the 8 in 8,420 is 10 times greater than the 8 in 6,870

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