Which one is greater of 99^50+100^50 and 101^509950+10050and10150?

1 Answer
Jul 13, 2018

101^50-99^50-100^5010150995010050

=(100+1)^50-(100-1)^50-100^50=(100+1)50(1001)5010050

=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