Práctica #3: Ciclos for

Activity Description

Solve the following set of problems using Python 3. Run and test each of your programs to make sure they work as expected.

All the following problems must be solved using for loops.

1. Write a program powers.py that prints a table of values of \(n\) and \(2^n\) for \(n = 1, 2, 3, \dots, 10\). You do not need to use any functions other than main().

   The program’s output should look like this:

   1 2
   2 4
   3 8
   4 16
   5 32
   6 64
   7 128
   8 256
   9 512
   10 1024

2. Write a program called table.py that prints a table of values \(n, \log n, n \log n, n^2,\) and \(2^n\) for \(n = 10, 20, 30, \ldots, 200\). The log function is in the math module. You do not need to use any functions other than main().

   The program’s output should look like this:

   10 2.302585092994046 23.02585092994046 100 1024
   20 2.995732273553991 59.914645471079815 400 1048576
   30 3.4011973816621555 102.03592144986466 900 1073741824
   40 3.6888794541139363 147.55517816455745 1600 1099511627776
   50 3.912023005428146 195.6011502714073 2500 1125899906842624
   60 4.0943445622221 245.66067373332604 3600 1152921504606846976
   70 4.248495242049359 297.39466694345515 4900 1180591620717411303424
   80 4.382026634673881 350.5621307739105 6400 1208925819614629174706176
   90 4.499809670330265 404.9828703297238 8100 1237940039285380274899124224
   100 4.605170185988092 460.51701859880916 10000 1267650600228229401496703205376
   110 4.700480365792417 517.0528402371658 12100 1298074214633706907132624082305024
   120 4.787491742782046 574.4990091338454 14400 1329227995784915872903807060280344576
   130 4.867534450455582 632.7794785592257 16900 1361129467683753853853498429727072845824
   140 4.941642422609304 691.8299391653026 19600 1393796574908163946345982392040522594123776
   150 5.0106352940962555 751.5952941144383 22500 1427247692705959881058285969449495136382746624
   160 5.075173815233827 812.0278104374122 25600 1461501637330902918203684832716283019655932542976
   170 5.135798437050262 873.0857342985446 28900 1496577676626844588240573268701473812127674924007424
   180 5.19295685089021 934.7322331602379 32400 1532495540865888858358347027150309183618739122183602176
   190 5.247024072160486 996.9345737104924 36100 1569275433846670190958947355801916604025588861116008628224
   200 5.298317366548036 1059.6634733096073 40000 1606938044258990275541962092341162602522202993782792835301376

3. Write a program temptable.py. The program should contain a function called fahrenheit_to_celsius(x) that converts x degrees Fahrenheit to its equivalent degrees Celsius. Remember that:

   $$ ^\circ C = \frac{5}{9}(^\circ F - 32) $$

   The main() function should print a table for temperatures between –30°F and 100°F at 10 degree intervals, with their corresponding conversion to degrees Celsius as returned by the fahrenheit_to_celsius(x) function.

   The program’s output should look like this:

   -30 °F = -34.44444444444444 °C
   -20 °F = -28.88888888888889 °C
   -10 °F = -23.333333333333332 °C
   0 °F = -17.77777777777778 °C
   10 °F = -12.222222222222221 °C
   20 °F = -6.666666666666667 °C
   30 °F = -1.1111111111111112 °C
   40 °F = 4.444444444444445 °C
   50 °F = 10.0 °C
   60 °F = 15.555555555555555 °C
   70 °F = 21.11111111111111 °C
   80 °F = 26.666666666666668 °C
   90 °F = 32.22222222222222 °C
   100 °F = 37.77777777777778 °C

4. Write a program disttable.py that prints a table of mile to kilometer conversions for distances between 100 and 1500 miles at 100 mile intervals. Write a function called miles_to_km(x) to do the conversion. One mile is approximately 1.609 km.

   The program’s output should look like this:

   100 miles = 160.9 km
   200 miles = 321.8 km
   300 miles = 482.7 km
   400 miles = 643.6 km
   500 miles = 804.5 km
   600 miles = 965.4 km
   700 miles = 1126.3 km
   800 miles = 1287.2 km
   900 miles = 1448.1 km
   1000 miles = 1609.0 km
   1100 miles = 1769.9 km
   1200 miles = 1930.8 km
   1300 miles = 2091.7 km
   1400 miles = 2252.6 km
   1500 miles = 2413.5 km
   

5. Write a program called basel.py. Define in this program a function called basel(n) that calculate the following series:

   $$ \sum_{k=1}^{n}\frac{1}{k^2} = \frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\cdots+\frac{1}{n^2} $$

   The program’s main() function should print a table with the values of basel(n) for \(n = 10, 100, 1000, \ldots, 10^7\). Hint: Use range() to create the exponents.

   The program’s output should look like this:

   10 1.5497677311665408
   100 1.6349839001848923
   1000 1.6439345666815615
   10000 1.6448340718480652
   100000 1.6449240668982423
   1000000 1.64493306684877
   10000000 1.6449339668472596

6. Write a program called pyramid.py. Define in this program a function pyramid(n) that returns \(1^2 + 2^2 + 3^2 + \cdots + n^2\). The program’s main() function should print a table with the values of pyramid(n) for \(n = 1, 2, 3, \ldots, 20.\)

   The program’s output should look like this:

   1 1
   2 5
   3 14
   4 30
   5 55
   6 91
   7 140
   8 204
   9 285
   10 385
   11 506
   12 650
   13 819
   14 1015
   15 1240
   16 1496
   17 1785
   18 2109
   19 2470
   20 2870