1/(1+√ 2)+1/( √2+ √3)+1/(√3+ √4)+……+1/(√98+√99)+1/(√99+ √100)
=(√2-1)/(2-1)+(√3-2)/(3-2).+(√99-√98)/(99-98)+(√100-√99)/(100-99)
=√2-1+√3-√2+...+√99-√98+(√100-√99)
=√100-1
=10-1
=9
1/1+√ 2+1/ √2+ √3+1/√3+ √4+……+1/√98+√99+1/√99+ √100 的值?
1个回答
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