Rezolvați (83!/81!+82!)(40!+41!/42!

$$( \frac{ 83 ! }{ 81 ! +82 ! } )( \frac{ 40 ! +41 ! }{ 42 ! }$$

Evaluați

$$2$$

Pașii soluției

Factorialul lui 83 este 39455239697206586511897471180120610571436503407643446275224357528369751562996629334879591940103770870906880000000000000000000.

$$\frac{39455239697206586511897471180120610571436503407643446275224357528369751562996629334879591940103770870906880000000000000000000}{81!+82!}\times \frac{40!+41!}{42!}$$

Factorialul lui 81 este 5797126020747367985879734231578109105412357244731625958745865049716390179693892056256184534249745940480000000000000000000.

$$\frac{39455239697206586511897471180120610571436503407643446275224357528369751562996629334879591940103770870906880000000000000000000}{5797126020747367985879734231578109105412357244731625958745865049716390179693892056256184534249745940480000000000000000000+82!}\times \frac{40!+41!}{42!}$$

Factorialul lui 82 este 475364333701284174842138206989404946643813294067993328617160934076743994734899148613007131808479167119360000000000000000000.

$$\frac{39455239697206586511897471180120610571436503407643446275224357528369751562996629334879591940103770870906880000000000000000000}{5797126020747367985879734231578109105412357244731625958745865049716390179693892056256184534249745940480000000000000000000+475364333701284174842138206989404946643813294067993328617160934076743994734899148613007131808479167119360000000000000000000}\times \frac{40!+41!}{42!}$$

Adunați 5797126020747367985879734231578109105412357244731625958745865049716390179693892056256184534249745940480000000000000000000 și 475364333701284174842138206989404946643813294067993328617160934076743994734899148613007131808479167119360000000000000000000 pentru a obține 481161459722031542828017941220983055749225651312724954575906799126460384914593040669263316342728913059840000000000000000000.

$$\frac{39455239697206586511897471180120610571436503407643446275224357528369751562996629334879591940103770870906880000000000000000000}{481161459722031542828017941220983055749225651312724954575906799126460384914593040669263316342728913059840000000000000000000}\times \frac{40!+41!}{42!}$$

Împărțiți 39455239697206586511897471180120610571436503407643446275224357528369751562996629334879591940103770870906880000000000000000000 la 481161459722031542828017941220983055749225651312724954575906799126460384914593040669263316342728913059840000000000000000000 pentru a obține 82.

$$82\times \frac{40!+41!}{42!}$$

Factorialul lui 40 este 815915283247897734345611269596115894272000000000.

$$82\times \frac{815915283247897734345611269596115894272000000000+41!}{42!}$$

Factorialul lui 41 este 33452526613163807108170062053440751665152000000000.

$$82\times \frac{815915283247897734345611269596115894272000000000+33452526613163807108170062053440751665152000000000}{42!}$$

Adunați 815915283247897734345611269596115894272000000000 și 33452526613163807108170062053440751665152000000000 pentru a obține 34268441896411704842515673323036867559424000000000.

$$82\times \frac{34268441896411704842515673323036867559424000000000}{42!}$$

Factorialul lui 42 este 1405006117752879898543142606244511569936384000000000.

$$82\times \frac{34268441896411704842515673323036867559424000000000}{1405006117752879898543142606244511569936384000000000}$$

Reduceți fracția \frac{34268441896411704842515673323036867559424000000000}{1405006117752879898543142606244511569936384000000000} la cei mai mici termeni, prin extragerea și reducerea 34268441896411704842515673323036867559424000000000.

$$82\times \frac{1}{41}$$

Înmulțiți 82 cu \frac{1}{41} pentru a obține \frac{82}{41}.

$$\frac{82}{41}$$

Împărțiți 82 la 41 pentru a obține 2.

$$2$$

Descompunere în factori

$$2$$