Larger of 9950 + 10050 and 10150 is

We have, 10150=(100+1)50 =10050+50⋅10049+50⋅491⋅2⋅10048+…and  9950=(100−1)50=10050−50⋅10049+50⋅491⋅2⋅10048−…Subtracting, we get 10150−9950=250⋅10049+50⋅49⋅481⋅2⋅3×10047+… =10050+2⋅50⋅49⋅481⋅2⋅3⋅10047+…>10050Hence, 10150>9950+10050