Which one is greater of #99^50+100^50 and 101^50#?

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Answer 1 · 2018-07-13T10:31:03

#101^50-99^50-100^50#

#=(100+1)^50-(100-1)^50-100^50#

#=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#