数学题100²-98²+96²-94²+···+4²-2²等于多少
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![数学题100²-98²+96²-94²+···+4²-2²等于多少](/uploads/image/z/353380-4-0.jpg?t=%E6%95%B0%E5%AD%A6%E9%A2%98100%26%23178%3B-98%26%23178%3B%2B96%26%23178%3B%EF%BC%8D94%26%23178%3B%2B%C2%B7%C2%B7%C2%B7%2B4%26%23178%3B%EF%BC%8D2%26%23178%3B%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91)
数学题100²-98²+96²-94²+···+4²-2²等于多少
数学题100²-98²+96²-94²+···+4²-2²等于多少
数学题100²-98²+96²-94²+···+4²-2²等于多少
100²-98²+96²-94²+···+4²-2²
=(100+98)(100-98)+(96+94)(96-94)+……+(4+2)(4-2)
=2×﹙100+98+96+94+……+4+2)
=2×2×﹙50+49+48+……+2+1)
=4×﹙50+1)×50÷2
=4×51×50÷2
=204×50÷2
=10200÷2
=5100
100²-98²+96²-94²+···+4²-2²
=(100+98)(100-98)+(96+94)(96-94)+...+(4+2)(4-2)
=2×(100+98+...+4+2)
=(100+2)×50
=5100
100²-98²+96²-94²+···+4²-2²
=(100+98)(100-98)+(96+94)(96-94)+……+(4+2)(4-2)
=2×﹙100+98+96+94+……+4+2)
=2×2×﹙50+49+48+……+2+1)
=4×﹙50+1)×50÷2
=5100