50²-49²+48²-47²+…+2²-1=
来源:学生作业帮助网 编辑:作业帮 时间:2024/08/09 22:10:31
![50²-49²+48²-47²+…+2²-1=](/uploads/image/z/3020476-4-6.jpg?t=50%26%23178%3B-49%26%23178%3B%2B48%26%23178%3B-47%26%23178%3B%2B%E2%80%A6%2B2%26%23178%3B-1%3D)
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50²-49²+48²-47²+…+2²-1=
50²-49²+48²-47²+…+2²-1=
50²-49²+48²-47²+…+2²-1=
50²-49²+48²-47²+…+2²-1
=(50+49)*(50-49)+(48+47)*(48-47)+…+(2+1)*(2-1)
=50+49+48+47+…+2+1
=(50+1)*50/2
=1275