Question

2×6×10+6×10×14+18+......+78×82×86=

Answer 1

问：2×6×10+6×10×14+18+......+78×82×86=

答：宝子可以补充一下题目吗

答：We can simplify this expression by factoring out 2×6×10 from each term in the sum:2×6×10+6×10×14+18+......+78×82×86= 2×6×10(1 + 7×14 + 9×13 + ... + 39×43)Now we need to find the sum of the arithmetic series in parentheses. We can use the formula for the sum of an arithmetic series:S = n/2(a₁ + aₙ)where S is the sum of the series, n is the number of terms in the series, a₁ is the first term, and aₙ is the nth term.In this case, the first term is 1, the last term is 39×43, and the commo

答：2×6×10+6×10×14+18+......+78×82×86我们可以将其简化为三元组的形式：(2×6×10) + (6×10×14) + (18) + ... + (78×82×86)= 2×(3×2)×(5×2) + 6×(5×2)×(7×2) + 18×(1) + ... + 78×(41)×(43)= 2×3×5×2×(1×10) + 6×5×7×2×(2×7) + 18×(1) + ... + 78×41×43×(82×86)= 60 + 420 + 18 + ... + (78×41×43×82×86)现在，我们可以使用等差数列求和公式来求出这些项的和：S = n/2 × (a + l)其中 S 是和，n 是项数，a 是首项，l 是末项。在这种情况下，我们有：a = 60（首项）l = 78×41×43×82×86（末项）d = 420 - 60 = 360（公差）n = (l - a)/d + 1（项数）将这些值代入公式中，我们得到：n = (78×41×43×82×86 - 60)/360 + 1 = 5947