设S=1+1/根号2+1/根号3+1/根号4+……+1/根号990025,则不超过x的最大整数为多少?为什么?
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![设S=1+1/根号2+1/根号3+1/根号4+……+1/根号990025,则不超过x的最大整数为多少?为什么?](/uploads/image/z/6940164-12-4.jpg?t=%E8%AE%BES%EF%BC%9D1%2B1%2F%E6%A0%B9%E5%8F%B72%2B1%2F%E6%A0%B9%E5%8F%B73%2B1%2F%E6%A0%B9%E5%8F%B74%2B%E2%80%A6%E2%80%A6%2B1%2F%E6%A0%B9%E5%8F%B7990025%2C%E5%88%99%E4%B8%8D%E8%B6%85%E8%BF%87x%E7%9A%84%E6%9C%80%E5%A4%A7%E6%95%B4%E6%95%B0%E4%B8%BA%E5%A4%9A%E5%B0%91%3F%E4%B8%BA%E4%BB%80%E4%B9%88%3F)
设S=1+1/根号2+1/根号3+1/根号4+……+1/根号990025,则不超过x的最大整数为多少?为什么?
设S=1+1/根号2+1/根号3+1/根号4+……+1/根号990025,则不超过x的最大整数为多少?为什么?
设S=1+1/根号2+1/根号3+1/根号4+……+1/根号990025,则不超过x的最大整数为多少?为什么?
s=1+1/√2+1/√3+1/√4+……+1/√(990025)
=1+2/(√2+√2)+2/(√3+√3)+……+2/[√(990025)+√(990025)]
=1+2*{1/(√2+√2)+1/(√3+√3)+……+1/[√(990025)+√(990025)]}
<1+2*{1/(√2+1)+1/(√3+√2)+……+1/[√(990025)+√(990025-1)]}
=1+2*{(√2-1)+(√3-√2)+……+[√(990025)-√(990025-1)]}
=1+2*[-1+√(990025)]
=1+2*(995-1)
=1989
即s<1989
又因为s>1+1/√2+1/√3+1/√4+……+1/√(990025-1)
=2/(√1+√1)+2/(√2+√2)+2/(√3+√3)+……+2/[√(990025-1)+√(990025-1)]
>2/(√2+√1)+2/(√3+√2)+2/(√4+√3)+……+2/[√(990025)+√(990025-1)]
=2*[(√2-√1)+(√3-√2)+(√4-√3)+……+[√(990025)-√(990025-1)]
=2*(-1+√(990025)]
=2*(995-1)
=1988
即s>1988
所以1988所以不超过s的最大整数为1988