计算50²-49²+48²-47²+…+4²-3²+2²-1²的值.
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/26 01:53:54
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计算50²-49²+48²-47²+…+4²-3²+2²-1²的值.
计算50²-49²+48²-47²+…+4²-3²+2²-1²的值.
计算50²-49²+48²-47²+…+4²-3²+2²-1²的值.
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
利用平方差公式
原式=(50+49)(50-49)+(48+47)(48-47)+......(2+1)(2-1)
=50+49+48+......+2+1
=1275
望采纳,亲