101^50-99^50-100^5010150−9950−10050
=(100+1)^50-(100-1)^50-100^50=(100+1)50−(100−1)50−10050
=2(""^50C_1*100^49+""^50C_3*100^47+""^50C_5*100^45+...+""^50C_49*100)-100^50
=2(""^50C_3*100^47+""^50C_5*100^45+...+""^50C_49*100) +2*""^50C_1*100^49-100^50
=2(""^50C_3*100^47+""^50C_5*100^45+...+""^50C_49*100) +100^50-100^50>0
Hence
101^50>100^50+99^50