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1×2+2×3+3×4+……+48×49+49×50等于多少?
人气:371 ℃ 时间:2020-05-10 05:05:43
解答
利用等式:
n(n+1) = (1/3)[(n+2)(n+1)(n) - (n+1)(n)(n-1)]
1×2+2×3+3×4+……+48×49+49×50
=(1/3)[(3×2×1 - 0) + (4×3×2 - 3×2×1) + ...+ (51×50×49 - 50×49×48)]
=(1/3)(51×50×49)(上步中前后抵消)
=41650
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