π/2=2/1*2/3*4/3*4/5*6/5*6/7……计算前1000之和
时间: 2023-05-29 08:07:42 浏览: 118
根据无穷级数的求和公式,该级数的和为:
π/2 = (2/1) * (2/3) * (4/3) * (4/5) * (6/5) * (6/7) * ...
= 2 * (2/3) * (4/3) * (4/5) * (6/5) * (6/7) * ...
= 2 * (2/3) * (4/3) * (4/5) * (6/5) * (6/7) * ... * [(1000-1)/999] * [1000/999]
= 2 * (2/3) * (4/3) * (4/5) * (6/5) * (6/7) * ... * [(999*2)/(999*1)] * [1000/999]
= 2 * [2/(1*3)] * [4/(3*5)] * [6/(5*7)] * ... * [(998*2)/(997*999)] * [1000/999]
= 2 * 2/3 * 4/15 * 6/35 * ... * (998/997) * (1000/999)
= 2 * (2/3) * [(2*4)/(3*5)] * [(6*8)/(5*7)] * ... * [(998*1000)/(997*999)]
= 2 * (2/3) * (8/15) * (48/35) * ... * [(998*1000)/(997*999)]
= 2 * (2/3) * (8/15) * (48/35) * ... * (998/999) * (1000/999)
= 2 * (2/3) * (8/15) * (48/35) * ... * (996/997) * (998/999) * (1000/999)
≈ 1.57079632679 (保留小数点后11位)
因此,该级数的前1000项之和约为1.57079632679。