提问一道初一数学思考题,(√2-1)×(√2+1)=1;(√3-√2) ×(√3+√2)=1;(√2005-√2004)×(√2005+2004)=1;(√2006-√2005)×(√2006+√2005)=1;利用上面规律计算:1/1+√2 + 1/√2+√3 +1/√3+√4 +…
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![提问一道初一数学思考题,(√2-1)×(√2+1)=1;(√3-√2) ×(√3+√2)=1;(√2005-√2004)×(√2005+2004)=1;(√2006-√2005)×(√2006+√2005)=1;利用上面规律计算:1/1+√2 + 1/√2+√3 +1/√3+√4 +…](/uploads/image/z/1273459-67-9.jpg?t=%E6%8F%90%E9%97%AE%E4%B8%80%E9%81%93%E5%88%9D%E4%B8%80%E6%95%B0%E5%AD%A6%E6%80%9D%E8%80%83%E9%A2%98%2C%28%E2%88%9A2-1%29%C3%97%28%E2%88%9A2%2B1%29%3D1%EF%BC%9B%28%E2%88%9A3-%E2%88%9A2%29+%C3%97%28%E2%88%9A3%2B%E2%88%9A2%29%3D1%EF%BC%9B%EF%BC%88%E2%88%9A2005-%E2%88%9A2004%EF%BC%89%C3%97%EF%BC%88%E2%88%9A2005%2B2004%EF%BC%89%3D1%EF%BC%9B%EF%BC%88%E2%88%9A2006-%E2%88%9A2005%EF%BC%89%C3%97%EF%BC%88%E2%88%9A2006%2B%E2%88%9A2005%EF%BC%89%3D1%EF%BC%9B%E5%88%A9%E7%94%A8%E4%B8%8A%E9%9D%A2%E8%A7%84%E5%BE%8B%E8%AE%A1%E7%AE%97%EF%BC%9A1%2F1%2B%E2%88%9A2+%2B+1%2F%E2%88%9A2%2B%E2%88%9A3+%2B1%2F%E2%88%9A3%2B%E2%88%9A4+%2B%E2%80%A6)
提问一道初一数学思考题,(√2-1)×(√2+1)=1;(√3-√2) ×(√3+√2)=1;(√2005-√2004)×(√2005+2004)=1;(√2006-√2005)×(√2006+√2005)=1;利用上面规律计算:1/1+√2 + 1/√2+√3 +1/√3+√4 +…
提问一道初一数学思考题,
(√2-1)×(√2+1)=1;(√3-√2) ×(√3+√2)=1;(√2005-√2004)×(√2005+2004)=1;(√2006-√2005)×(√2006+√2005)=1;利用上面规律计算:1/1+√2 + 1/√2+√3 +1/√3+√4 +……+1/√2004+√2005 + 1/√2005+√2006答案是√2006-1.
提问一道初一数学思考题,(√2-1)×(√2+1)=1;(√3-√2) ×(√3+√2)=1;(√2005-√2004)×(√2005+2004)=1;(√2006-√2005)×(√2006+√2005)=1;利用上面规律计算:1/1+√2 + 1/√2+√3 +1/√3+√4 +…
题目你没写括号吧?应该是
1/(1+√2)+1/(√2+√3)+……+1/(√2005+√2006)
=(√2-1)+(√3-√2)+……+(√2006-√2005)
=√2006-1
肯定题目错了,二楼正解
因为(√2-1)×(√2+1)=1
所以1/1+√2=√2-1 (1)
同理1/√2+√3=√3-√2 (2)
.........
1/√2005+√2006=√2006-√2005 (2005)
将(1)+(2)+.........+(2005)=√2006-1
原式=(√2-1)×(√2+1)/1+√2+(√3-√2) ×(√3+√2)/√2+√3 +(√4-√3) ×(√4+√3) √3+√4+……+(√2006-√2005)×(√2006+√2005)/√2005+√2006=√2-1+√3-√2+√4-√3+……+√2006-√2005=-1+√2006=√2006-1