100²-99²+98²-97²+.+2²-1用简便方法怎么算
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![100²-99²+98²-97²+.+2²-1用简便方法怎么算](/uploads/image/z/116655-15-5.jpg?t=100%26%23178%3B-99%26%23178%3B%2B98%26%23178%3B-97%26%23178%3B%2B.%2B2%26%23178%3B-1%E7%94%A8%E7%AE%80%E4%BE%BF%E6%96%B9%E6%B3%95%E6%80%8E%E4%B9%88%E7%AE%97)
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100²-99²+98²-97²+.+2²-1用简便方法怎么算
100²-99²+98²-97²+.+2²-1用简便方法怎么算
100²-99²+98²-97²+.+2²-1用简便方法怎么算
100²-99²+98²-97²+.+2²-1
=(100+99)x(100-99)+(98+97)x(98-97)+.+(2+1)x(2-1)
=(100+99)x1+(98+97)x1+.+(2+1)x1
=100+99+98+97+.+2+1
=(100+1)x100÷2
=101x50
=5050
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