حل (83!/81!+82!)(40!+41!/42!

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

ارزیابی

$$2$$

مراحل راه‌حل

فاکتوریل 83 عبارت است از 39455239697206586511897471180120610571436503407643446275224357528369751562996629334879591940103770870906880000000000000000000.

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

فاکتوریل 81 عبارت است از 5797126020747367985879734231578109105412357244731625958745865049716390179693892056256184534249745940480000000000000000000.

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

فاکتوریل 82 عبارت است از 475364333701284174842138206989404946643813294067993328617160934076743994734899148613007131808479167119360000000000000000000.

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

5797126020747367985879734231578109105412357244731625958745865049716390179693892056256184534249745940480000000000000000000 و 475364333701284174842138206989404946643813294067993328617160934076743994734899148613007131808479167119360000000000000000000 را برای دریافت 481161459722031542828017941220983055749225651312724954575906799126460384914593040669263316342728913059840000000000000000000 اضافه کنید.

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

39455239697206586511897471180120610571436503407643446275224357528369751562996629334879591940103770870906880000000000000000000 را بر 481161459722031542828017941220983055749225651312724954575906799126460384914593040669263316342728913059840000000000000000000 برای به دست آوردن 82 تقسیم کنید.

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

فاکتوریل 40 عبارت است از 815915283247897734345611269596115894272000000000.

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

فاکتوریل 41 عبارت است از 33452526613163807108170062053440751665152000000000.

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

815915283247897734345611269596115894272000000000 و 33452526613163807108170062053440751665152000000000 را برای دریافت 34268441896411704842515673323036867559424000000000 اضافه کنید.

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

فاکتوریل 42 عبارت است از 1405006117752879898543142606244511569936384000000000.

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

کسر \frac{34268441896411704842515673323036867559424000000000}{1405006117752879898543142606244511569936384000000000} را با ریشه گرفتن و ساده کردن 34268441896411704842515673323036867559424000000000، به کمترین عبارت‌ها کاهش دهید.

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

82 و \frac{1}{41} را برای دستیابی به \frac{82}{41} ضرب کنید.

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

82 را بر 41 برای به دست آوردن 2 تقسیم کنید.

$$2$$

عامل

$$2$$