Which of the following is larger 
99^50+100^50 or 101^50 
The part of the answer that is given in the photo please explain. How can we take 100^50 common?
= 2 [ C 1 50 ( 100 ) 49 + C 3 50 ( 100 ) 47 + . . . . . ] = 2 [ 50 ( 100 ) 49 + C 3 50 ( 100 ) 47 + . . . . ] = 100 50 + o t h e r   p o s i t i v e   t e r m s > 100 50
S o , 101 50 - 99 50 > 100 50 , i . e . , 101 50 > 99 50 + 100 50 H e n c e , 101 50 i s   l a r g e r   t h a n   99 50 + 100 50
 

Hi, Lets take = 25010049+50C310047+.....=100×10049+2×50C310047+......=1001×10049+2×50!3!×47!10047+......=10050+2×50!3!×47!10047+......So here 10050+2×50!3!×47!10047+...... must be greater than 10050 because all the rest term will be positive and hence make it greater than 10050 so here 10050 is not taken as common but it is used for conclusion

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