billwalster

Dr. G. William Walster

5 Reputation

One Badge

12 years, 251 days

MaplePrimes Activity


These are answers submitted by billwalster


Here is another way.

restart

with(plots):

``

delta := 0.5

.5

(1)

alpha := proc(n);
1/(1 + n)
end proc;

proc (n) 1/(n+1) end proc

(2)

D1 := proc(n);
product(3*delta*alpha(k) - alpha(k) + 1, k = 1 .. n) - product(1 - alpha(k)*(1 - delta), k = 1 .. n)
end proc;

proc (n) product(3*delta*alpha(k)-alpha(k)+1, k = 1 .. n)-product(1-alpha(k)*(1-delta), k = 1 .. n) end proc

(3)

 

 

points:= {seq([alpha(n), D1(n)], n = 1 .. 100)};

{[1/2, .5000000000], [1/3, .8333333340], [1/4, 1.093750001], [1/5, 1.312500001], [1/6, 1.503906250], [1/7, 1.675781250], [1/8, 1.832885742], [1/9, 1.978352865], [1/10, 2.114364624], [1/11, 2.242507934], [1/12, 2.363977114], [1/13, 2.479696273], [1/14, 2.590397000], [1/15, 2.696669697], [1/16, 2.798998681], [1/17, 2.897786871], [1/18, 2.993373591], [1/19, 3.086047695], [1/20, 3.176057419], [1/21, 3.263617900], [1/22, 3.348917005], [1/23, 3.432119910], [1/24, 3.513372748], [1/25, 3.592805523], [1/26, 3.670534488], [1/27, 3.746664093], [1/28, 3.821288585], [1/29, 3.894493346], [1/30, 3.966356022], [1/31, 4.036947451], [1/32, 4.106332486], [1/33, 4.174570659], [1/34, 4.241716786], [1/35, 4.307821461], [1/36, 4.372931509], [1/37, 4.437090351], [1/38, 4.500338351], [1/39, 4.562713104], [1/40, 4.624249695], [1/41, 4.684980929], [1/42, 4.744937531], [1/43, 4.804148322], [1/44, 4.862640386], [1/45, 4.920439211], [1/46, 4.977568815], [1/47, 5.034051867], [1/48, 5.089909781], [1/49, 5.145162820], [1/50, 5.199830175], [1/51, 5.253930052], [1/52, 5.307479725], [1/53, 5.360495615], [1/54, 5.412993345], [1/55, 5.464987792], [1/56, 5.516493130], [1/57, 5.567522892], [1/58, 5.618089990], [1/59, 5.668206759], [1/60, 5.717885006], [1/61, 5.767136028], [1/62, 5.815970647], [1/63, 5.864399235], [1/64, 5.912431739], [1/65, 5.960077711], [1/66, 6.007346322], [1/67, 6.054246388], [1/68, 6.100786383], [1/69, 6.146974471], [1/70, 6.192818503], [1/71, 6.238326052], [1/72, 6.283504402], [1/73, 6.328360597], [1/74, 6.372901425], [1/75, 6.417133437], [1/76, 6.461062958], [1/77, 6.504696107], [1/78, 6.548038800], [1/79, 6.591096757], [1/80, 6.633875510], [1/81, 6.676380420], [1/82, 6.718616669], [1/83, 6.760589283], [1/84, 6.802303140], [1/85, 6.843762961], [1/86, 6.884973325], [1/87, 6.925938680], [1/88, 6.966663345], [1/89, 7.007151511], [1/90, 7.047407246], [1/91, 7.087434498], [1/92, 7.127237122], [1/93, 7.166818847], [1/94, 7.206183312], [1/95, 7.245334054], [1/96, 7.284274510], [1/97, 7.323008036], [1/98, 7.361537895], [1/99, 7.399867260], [1/100, 7.437999229], [1/101, 7.475936819]}

(4)

 

pointplot(points);

 

 


 

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