Home » Archimedes archive » Archimedes World » AW-1996-07.adf » !Ignotum_Ignotum » !Ignotum/Formulae/Seri
!Ignotum/Formulae/Seri
This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.
Some of these files were originally commercial releases in the 1980s and 1990s, but they are now widely available online. I assume that copyright over them is no longer being asserted. If you own the copyright and would like files to be removed, please contact me.
| Tape/disk: | Home » Archimedes archive » Archimedes World » AW-1996-07.adf » !Ignotum_Ignotum |
| Filename: | !Ignotum/Formulae/Seri |
| Read OK: | ✔ |
| File size: | 03D5 bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
# Maths > Series nth term=a+(n-1)d For an arithmetic progression, eg 1 3 5 7 9 etc. a=starting number (eg 1) d=common difference (eg 2) S<n>=(n/2)(2a+(n-1)d) For an arithmetic progression, eg 1 3 5 7 9 etc. S<n>=sum of the numbers up to term n. a=starting number (eg 1) d=common difference (eg 2) nth term=ar^(n-1) For a geometric progression, eg 1 2 4 8 16 a=starting number (eg 1) r=common ratio (eg 2) S<n>=a(1-r^n)/(1-r) For a geometric progression, eg 1 2 4 8 16 S<n>=sum of the numbers up to term n. a=starting number (eg 1) r=common ratio (eg 2) S<i>=a/(1-r) For a geometric progression, when |r|<1, eg 1 1/2 1/4 1/8 1/16 S<i>=sum of terms to infinity a=starting number (eg 1) r=common ratio (eg �) e=(1/0!)+(1/1!)+(1/2!)+(1/3!)+(1/4!)... This is one way of calculating e (2.718), where a! is the factorial of a: a(a-1)(a-2)(a-3).. until a-n=1 Note: 0!=1
00000000 23 20 4d 61 74 68 73 20 3e 20 53 65 72 69 65 73 |# Maths > Series| 00000010 0a 6e 74 68 20 74 65 72 6d 3d 61 2b 28 6e 2d 31 |.nth term=a+(n-1| 00000020 29 64 0a 46 6f 72 20 61 6e 20 61 72 69 74 68 6d |)d.For an arithm| 00000030 65 74 69 63 20 70 72 6f 67 72 65 73 73 69 6f 6e |etic progression| 00000040 2c 20 65 67 20 31 20 33 20 35 20 37 0a 39 20 65 |, eg 1 3 5 7.9 e| 00000050 74 63 2e 0a 61 3d 73 74 61 72 74 69 6e 67 20 6e |tc..a=starting n| 00000060 75 6d 62 65 72 20 28 65 67 20 31 29 0a 64 3d 63 |umber (eg 1).d=c| 00000070 6f 6d 6d 6f 6e 20 64 69 66 66 65 72 65 6e 63 65 |ommon difference| 00000080 20 28 65 67 20 32 29 0a 0a 53 3c 6e 3e 3d 28 6e | (eg 2)..S<n>=(n| 00000090 2f 32 29 28 32 61 2b 28 6e 2d 31 29 64 29 0a 46 |/2)(2a+(n-1)d).F| 000000a0 6f 72 20 61 6e 20 61 72 69 74 68 6d 65 74 69 63 |or an arithmetic| 000000b0 20 70 72 6f 67 72 65 73 73 69 6f 6e 2c 20 65 67 | progression, eg| 000000c0 20 31 20 33 20 35 20 37 0a 39 20 65 74 63 2e 0a | 1 3 5 7.9 etc..| 000000d0 53 3c 6e 3e 3d 73 75 6d 20 6f 66 20 74 68 65 20 |S<n>=sum of the | 000000e0 6e 75 6d 62 65 72 73 20 75 70 20 74 6f 20 74 65 |numbers up to te| 000000f0 72 6d 20 6e 2e 0a 61 3d 73 74 61 72 74 69 6e 67 |rm n..a=starting| 00000100 20 6e 75 6d 62 65 72 20 28 65 67 20 31 29 0a 64 | number (eg 1).d| 00000110 3d 63 6f 6d 6d 6f 6e 20 64 69 66 66 65 72 65 6e |=common differen| 00000120 63 65 20 28 65 67 20 32 29 0a 6e 74 68 20 74 65 |ce (eg 2).nth te| 00000130 72 6d 3d 61 72 5e 28 6e 2d 31 29 0a 46 6f 72 20 |rm=ar^(n-1).For | 00000140 61 20 67 65 6f 6d 65 74 72 69 63 20 70 72 6f 67 |a geometric prog| 00000150 72 65 73 73 69 6f 6e 2c 20 65 67 20 31 20 32 20 |ression, eg 1 2 | 00000160 34 20 38 20 31 36 0a 61 3d 73 74 61 72 74 69 6e |4 8 16.a=startin| 00000170 67 20 6e 75 6d 62 65 72 20 28 65 67 20 31 29 0a |g number (eg 1).| 00000180 72 3d 63 6f 6d 6d 6f 6e 20 72 61 74 69 6f 20 28 |r=common ratio (| 00000190 65 67 20 32 29 0a 0a 0a 53 3c 6e 3e 3d 61 28 31 |eg 2)...S<n>=a(1| 000001a0 2d 72 5e 6e 29 2f 28 31 2d 72 29 0a 46 6f 72 20 |-r^n)/(1-r).For | 000001b0 61 20 67 65 6f 6d 65 74 72 69 63 20 70 72 6f 67 |a geometric prog| 000001c0 72 65 73 73 69 6f 6e 2c 20 65 67 20 31 20 32 20 |ression, eg 1 2 | 000001d0 34 20 38 20 31 36 0a 53 3c 6e 3e 3d 73 75 6d 20 |4 8 16.S<n>=sum | 000001e0 6f 66 20 74 68 65 20 6e 75 6d 62 65 72 73 20 75 |of the numbers u| 000001f0 70 20 74 6f 20 74 65 72 6d 20 6e 2e 0a 61 3d 73 |p to term n..a=s| 00000200 74 61 72 74 69 6e 67 20 6e 75 6d 62 65 72 20 28 |tarting number (| 00000210 65 67 20 31 29 0a 72 3d 63 6f 6d 6d 6f 6e 20 72 |eg 1).r=common r| 00000220 61 74 69 6f 20 28 65 67 20 32 29 0a 0a 53 3c 69 |atio (eg 2)..S<i| 00000230 3e 3d 61 2f 28 31 2d 72 29 0a 46 6f 72 20 61 20 |>=a/(1-r).For a | 00000240 67 65 6f 6d 65 74 72 69 63 20 70 72 6f 67 72 65 |geometric progre| 00000250 73 73 69 6f 6e 2c 20 77 68 65 6e 20 7c 72 7c 3c |ssion, when |r|<| 00000260 31 2c 0a 65 67 20 31 20 31 2f 32 20 31 2f 34 20 |1,.eg 1 1/2 1/4 | 00000270 31 2f 38 20 31 2f 31 36 0a 53 3c 69 3e 3d 73 75 |1/8 1/16.S<i>=su| 00000280 6d 20 6f 66 20 74 65 72 6d 73 20 74 6f 20 69 6e |m of terms to in| 00000290 66 69 6e 69 74 79 0a 61 3d 73 74 61 72 74 69 6e |finity.a=startin| 000002a0 67 20 6e 75 6d 62 65 72 20 28 65 67 20 31 29 0a |g number (eg 1).| 000002b0 72 3d 63 6f 6d 6d 6f 6e 20 72 61 74 69 6f 20 28 |r=common ratio (| 000002c0 65 67 20 bd 29 0a 65 3d 28 31 2f 30 21 29 2b 28 |eg .).e=(1/0!)+(| 000002d0 31 2f 31 21 29 2b 28 31 2f 32 21 29 2b 28 31 2f |1/1!)+(1/2!)+(1/| 000002e0 33 21 29 2b 28 31 2f 34 21 29 2e 2e 2e 0a 54 68 |3!)+(1/4!)....Th| 000002f0 69 73 20 69 73 20 6f 6e 65 20 77 61 79 20 6f 66 |is is one way of| 00000300 20 63 61 6c 63 75 6c 61 74 69 6e 67 20 65 20 28 | calculating e (| 00000310 32 2e 37 31 38 29 2c 0a 77 68 65 72 65 20 61 21 |2.718),.where a!| 00000320 20 69 73 20 74 68 65 20 66 61 63 74 6f 72 69 61 | is the factoria| 00000330 6c 20 6f 66 20 61 3a 0a 61 28 61 2d 31 29 28 61 |l of a:.a(a-1)(a| 00000340 2d 32 29 28 61 2d 33 29 2e 2e 20 75 6e 74 69 6c |-2)(a-3).. until| 00000350 20 61 2d 6e 3d 31 0a 4e 6f 74 65 3a 20 30 21 3d | a-n=1.Note: 0!=| 00000360 31 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a |1...............| 00000370 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a |................| * 000003d0 0a 0a 0a 0a 0a |.....| 000003d5
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