50²-49²+48²-47²＋…＋4²－3²＋2²－1²
=(50+49)(50-49)+(48+47)(48-47)+……+(4+3)(4-3)+(2+1)(2-1)
=50+49+48+47+……+4+3+2+1
=(50+1)×50÷2
=1275