100²-99²+98²-97²+······+2²-1²=（ )

来源：学生作业帮助网编辑：作业帮时间：2024/05/02 17:00:52

100²-99²+98²-97²+······+2²-1²=（ )
100²-99²+98²-97²+······+2²-1²=（ )

100²-99²+98²-97²+······+2²-1²=（ )
=(100+99)x(100-99)+(98+97)x(98-97)+.+(2+1)(2-1)
=100+99+98+97+.+2+1
=101x50
=5050