다음을 풀어보세요: (83!/81!+82!)(40!+41!/42!

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

계산

$$2$$

해답 단계

83의 계승은 39455239697206586511897471180120610571436503407643446275224357528369751562996629334879591940103770870906880000000000000000000입니다.

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

81의 계승은 5797126020747367985879734231578109105412357244731625958745865049716390179693892056256184534249745940480000000000000000000입니다.

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

82의 계승은 475364333701284174842138206989404946643813294067993328617160934076743994734899148613007131808479167119360000000000000000000입니다.

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

5797126020747367985879734231578109105412357244731625958745865049716390179693892056256184534249745940480000000000000000000과(와) 475364333701284174842138206989404946643813294067993328617160934076743994734899148613007131808479167119360000000000000000000을(를) 더하여 481161459722031542828017941220983055749225651312724954575906799126460384914593040669263316342728913059840000000000000000000을(를) 구합니다.

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

39455239697206586511897471180120610571436503407643446275224357528369751562996629334879591940103770870906880000000000000000000을(를) 481161459722031542828017941220983055749225651312724954575906799126460384914593040669263316342728913059840000000000000000000(으)로 나눠서 82을(를) 구합니다.

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

40의 계승은 815915283247897734345611269596115894272000000000입니다.

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

41의 계승은 33452526613163807108170062053440751665152000000000입니다.

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

815915283247897734345611269596115894272000000000과(와) 33452526613163807108170062053440751665152000000000을(를) 더하여 34268441896411704842515673323036867559424000000000을(를) 구합니다.

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

42의 계승은 1405006117752879898543142606244511569936384000000000입니다.

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

34268441896411704842515673323036867559424000000000을(를) 추출 및 상쇄하여 분수 \frac{34268441896411704842515673323036867559424000000000}{1405006117752879898543142606244511569936384000000000}을(를) 기약 분수로 약분합니다.

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

82과(와) \frac{1}{41}을(를) 곱하여 \frac{82}{41}(을)를 구합니다.

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

82을(를) 41(으)로 나눠서 2을(를) 구합니다.

$$2$$

인수 분해

$$2$$