Determine whether the series is convergent or divergent by expressing sn as a telescoping sum (as in this example). [infinity] 6 n(n + 3) n = 1 a) convergent

b) divergent

If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.)

I assume the series is supposed to be

The summand can be expanded into partial fractions:

Then the sum is equivalent to

Consider the N-th partial sum of the series:

2[(1 - 1/4) + (1/2 - 1/5) + (1/3 - 1/6) + (1/4 - 1/7) + (1/5 - 1/8) + …

+ (1/(N - 3) - 1/N) + (1/(N - 2) - 1/(N + 1)) + (1/(N - 1) - 1/(N + 2)) + (1/N - 1/(N + 3))]

Each of the negative terms (in bold) will have a positive counterpart (underlined) that cancel, so the N-th partial sum would be

As N approaches infinity, the last three terms in the sum converge to 0, so the original sum converges to

this story was prepared by jim

mccullaugh in los angeles and

al stewart in new york.

new york the colossal success of "top gun" appears to have dramatically altered madison avenue's

perception of corporate sponsorship

of home video projects.

the paramount home video re- lease, featuring a 60- second diet

pepsi spot, was by no means the

first prerecorded video to carry an advertiser's plug, but it was the

first major theatrical release to do so. in the aftermath of the title's

success, paramount is widely ex- pected to ink a similar deal for

"crocodile dundee" or "star trek

iv" or both.

corporate america's new attraccds push british

recording sales

to 19% gain

london fueled by the compact

disk boom, the value of u.k. manu- facturer shipments of recordings

rose 19% in the 12 -month period ended march 1987, according to the

british phonographic industry.

total value of u.k. shipments for

the period was $755 million for all

configurations. (all value figures

are based on an exchange rate of

$1.68 to the pound sterling.)

cd sales totaled 10.7 million units

worth $121.3 million- compared

with 3.7 million units worth $39.5

million in the prior 12 months -and

accounted for two -thirds of the

overall gain in trade value. at present growth rates, says the bpi, cd

sales for calendar 1987 will reach 20

(continued on page 79)

step-by-step explanation:

let y equal to

the total fare and x is the mile of taxi ride. so the equation is

y = 0.55x + 1.75

since susie has

$10 to spend for a taxi cab, so he can have

10 = 0.55x +

1.75

x = 15 miles of

taxi ride

so the system of

inequality is

10 < 0.55x +

1.75

x > 2