1*3*5+5*7*9+……97*99*101
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1*3*5+5*7*9+……97*99*101
![1*3*5+5*7*9+……97*99*101](/uploads/image/z/3159355-67-5.jpg?t=1%2A3%2A5%2B5%2A7%2A9%2B%E2%80%A6%E2%80%A697%2A99%2A101)
待求和式=∑(4n+1)(4n+3)(4n+5),n从0到24.
用裂项相消法,
(4n+1)(4n+3)(4n+5) = 1/8 *[(4n+1)(4n+3)(4n+5)(4n+7) - (4n-1)(4n+1)(4n+3)(4n+5)]
所以∑(4n+1)(4n+3)(4n+5),n从0到24
=1/8 * [97*99*101*103 - (-1)*1*3*5]
=1/8 *[999* 10^5 + 24]
=12487503
用裂项相消法,
(4n+1)(4n+3)(4n+5) = 1/8 *[(4n+1)(4n+3)(4n+5)(4n+7) - (4n-1)(4n+1)(4n+3)(4n+5)]
所以∑(4n+1)(4n+3)(4n+5),n从0到24
=1/8 * [97*99*101*103 - (-1)*1*3*5]
=1/8 *[999* 10^5 + 24]
=12487503
1*3*5+5*7*9+……97*99*101
1+3+5+7+9+……+97+99是多少?
1-3+5-7+9-11……+97-99
求值,-1+3-5+7-9+……-97+99
1+3+5+7+9+…+95+97+99.
计算:-1-3-5-7-9…-97-99
1-3+5-7+9-11+…97+(-99)
1+3+5+7+9+…+97+99+100.
1/1*3+1/3*5+1/5*7+……+1/97*99+1/99*101
1-2+3-4+5-6+7-……+97-98+99-100+101怎么算
1/3*5+1/5*7+1/7*9+……1/97*99
1/3+1/3×5+1/5×7+1/7×9+…+1/97×99+1/99×101=?怎么计算的?