sisaira-sankalan

ganiteeya vishleshan mein, sisairo sankalan saamaanya arthon mein abhisran naheen karne vaale anant sankalan ko maan nirdisht karta hai jo maanak sankalan ke saath sanniptit hota hai yadi vah abhisaari ho. sisaira sankalan shreni ke aanshik sankalan ke samaantar maadhya ke seemaant maan ke roop mein paribhaashit hota hai.

sisaira sankalan ka naamakaran itaalavi vishleshak arnesto sisaira (1859–1906) ke sammaan mein rakha gaya.

anukram

paribhaasha

maana {an} ek anukram hai aur maana

shreni ka kvaaain aanshik sankalan hai

shreni sisaira yog ke saath sisaira sankalaneeya kahalaati hai yadi iske aanshik sankalanon ke yog ka maadhya , ki or agrasar ho:

anya shabdon mein, kisi anant shreni ka sisaira sankalan shreni ke pratham n aanshik sankalanon ka samaantar maadhya (ausat) ka seemaant maan hota hai jabki n anant ki or agrasar ho. yeh siddh kiya ja sakta hai ki abhisaari shreni sisaira sankalaneeya hoti hai aur shreni ka kul yog sisaira sankalan ke samaan hota hai. haalaanki, nimnalikhit udaaharan ullikheet karta hai ki shreni apasaari hai lekin sisaira sankalaneeya hai.

udaaharan

maana n ≥ 1 ke liye an = (−1)n+1 hai. arthaat {an} ek anukram hai

aur maana G ek shreni ko nirupit karta hai.

tab aanshik sankalanon {sn} ka anukram nimnalikhit hoga

is shreni G ko graandi shreni ke roop mein jaana jaata hai jo abhisaari naheen hai. anya roop mein, {sn} ke padon ke (aanshik) maadhya anukram {tn} hai jahaaain

nimn prakaar hain

at:

isliye shreni G ka sisaira sankalan ka maan 1/2 hai.

anya roop mein, maana n ≥ 1 ke liye an = n hai. arthaat {an} ek anukram hai.

aur maana G ek shreni ko nirupit karta hai.

tab {sn} ke aanshik sankalanon ka anukram

hoga aur G ka maan anant ki or apasarit hoga.

{tn } ke aanshik sankalanon ke maadhya ke anukram ke pad nimn prakaar honge:

at:, yeh anukram G ki tarah anant ki or apasaran karta hai tatha ab G sisaira sankalaneeya naheen hai.


ye bhi dekhein

  • haabil sankalan sootr
  • apasari shreni
  • aayalar sankalan
  • sisera maadhya
  • reej maadhya
  • fejar-prameya
  • laimbart sankalan

sandarbh