ลำด, บเลขคณ, ในทางคณ, ตศาสตร, งกฤษ, arithmetic, progression, arithmetic, sequence, อลำด, บของจำนวนซ, งผลต, างของสมาช, กสองต, วใด, อย, ดก, นในลำด, บเป, นค, าคงต, วเสมอ, เร, ยกค, าคงต, วน, นว, ผลต, างร, วม, common, difference, วอย, างเช, ลำด, เป, นท, ผลต, างร, ว. inthangkhnitsastr ladbelkhkhnit xngkvs arithmetic progression arithmetic sequence khuxladbkhxngcanwnsungphltangkhxngsmachiksxngtwid thixyutidkninladbepnkhakhngtwesmx eriykkhakhngtwnnwa phltangrwm common difference twxyangechn ladb 3 5 7 9 11 13 epnladbelkhkhnitthimiphltangrwmethakb 2thahakphcnerimtnkhxngladbelkhkhnitladbhnungkhux a1 aelamiphltangrwmkhxngsmachikthixyutidknethakb d aelwphcnthi n khxngladbnikhux a n a 1 n 1 d displaystyle a n a 1 n 1 d dd hruxinkrnithwip caid a n a m n m d displaystyle a n a m n m d dd hruxekhiyniddwyrupaebbkhwamsmphnthewiynekid a n a n 1 d displaystyle a n a n 1 d dd enuxha 1 phlrwm 1 1 phisucn 2 phlkhun 3 xangxing 4 duephim 5 aehlngkhxmulxunphlrwm aekikh2 5 8 11 14 4014 11 8 5 2 4016 16 16 16 16 80withikarkhanwnphlrwm 2 5 8 11 14 odyekhiynxnukrmklbhnamahlngaelabwkekhakbaetlaphcn phlrwmthiidcaepnladbkhngtwthiethakbphlbwkkhxngphcnaerkaelaphcnsudthay 2 14 16 thaihid 16 5 80 sungepnsxngethakhxngphlrwm phlrwmkhxngsmachikinladbelkhkhnit eriykwa xnukrmelkhkhnit xngkvs arithmetic series twxyangechn phicarnaphlrwm 2 5 8 11 14 displaystyle 2 5 8 11 14 phmrwmkhxngladbelkhkhnitkhangtnsamarthhaidxyangrwderw odyih n aethncanwnphcnthnghmd inkrninikhux 5 aelwkhundwyphlbwkkhxngphcnaerkaelaphcnsudthayinladbelkhkhnit inkrninikhux 2 14 16 aelasudthayhardwy 2 n a 1 a n 2 displaystyle frac n a 1 a n 2 inkrninicaidkhakhxngphlrwmkhux 2 5 8 11 14 5 2 14 2 5 16 2 40 displaystyle 2 5 8 11 14 frac 5 2 14 2 frac 5 times 16 2 40 sutrniichidsahrbthukladbelkhkhnitthimiphcnaerkaelaphcnsudthaykhux a 1 displaystyle a 1 aela a n displaystyle a n id phisucn aekikh xnukrmkhangtnsamarthekhiyninrupthismmulknidsxngaebb idaek S n a 1 a 1 d a 1 2 d a 1 n 2 d a 1 n 1 d displaystyle S n a 1 a 1 d a 1 2d cdots a 1 n 2 d a 1 n 1 d S n a n n 1 d a n n 2 d a n 2 d a n d a n displaystyle S n a n n 1 d a n n 2 d cdots a n 2d a n d a n dd bwksxngsmkarkhangtnekhadwykn thukphcnthiekiywkhxngkb d cahayip aelaehluxephiyng 2 S n n a 1 a n displaystyle 2S n n a 1 a n dd cdrupaebbihm aelainemuxerathrabaelwwa a n a 1 n 1 d displaystyle a n a 1 n 1 d dngnneracaid S n n a 1 a n 2 n 2 a 1 n 1 d 2 displaystyle S n frac n a 1 a n 2 frac n 2a 1 n 1 d 2 dd phlkhun aekikhphlkhunkhxngsmachikinladbelkhkhnit odyerimtngaetphcn a1 ipthung an sungmiphltangrwmethakb d samarthkhanwnidcak a 1 a 2 a n d n a 1 d n d n G a 1 d n G a 1 d displaystyle a 1 a 2 cdots a n d n left frac a 1 d right overline n d n frac Gamma left a 1 d n right Gamma left a 1 d right dd odythisylksn x n displaystyle x overline n hmaythungphlkhunladbephim rising sequential product aela G x displaystyle Gamma x aethnfngkchnaekmma xyangirktamsutrnicaichnganimidemux a 1 d displaystyle a 1 d epncanwnetmlbhruxsunyniepnrupaebbthwip sungekidkhuncakkarkhunsmachikkhxngladbelkhkhnit 1 2 n thiidniyamiwaelwinaefkthxeriyl n dngnnphlkhunkhxngladbni m m 1 m 2 n 2 n 1 n displaystyle m times m 1 times m 2 times cdots times n 2 times n 1 times n dd camikhaethakb n m 1 displaystyle frac n m 1 dd odythi m aela n epncanwnetmbwkxangxing aekikhSigler Laurence E trans 2002 Fibonacci s Liber Abaci Springer Verlag pp 259 260 ISBN 0 387 95419 8 duephim aekikhladberkhakhnit xnukrmaehlngkhxmulxun aekikhexrik dbebilyu iwssitn Arithmetic progression cakaemthewild exrik dbebilyu iwssitn Arithmetic series cakaemthewild ekhathungcak https th wikipedia org w index php title ladbelkhkhnit amp oldid 9488079, wikipedia, วิกิ หนังสือ, หนังสือ, ห้องสมุด,