Đại số lớp 6

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Hải Đăng

Bài 1:Tính tổng

a) \(\dfrac{2}{1.3}\) + \(\dfrac{2}{3.5}\) + \(\dfrac{2}{5.7}\) +......+\(\dfrac{2}{99.101}\)

b)\(\dfrac{5}{1.3}\) + \(\dfrac{5}{3.5}\) + \(\dfrac{5}{5.7}\) +.......+\(\dfrac{5}{99.101}\)

Dấu chấm là dấu nhân nhé các bạn.ok

Nguyễn Trần Thành Đạt
26 tháng 5 2017 lúc 14:43

a, \(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{99.101}\\ =1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}\\ =1-\dfrac{1}{101}=\dfrac{100}{101}\)

Nguyễn Huy Tú
26 tháng 5 2017 lúc 14:54

b, \(\dfrac{5}{1.3}+\dfrac{5}{3.5}+...+\dfrac{5}{99.101}\)

\(=\dfrac{5}{2}\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{2}{99.101}\right)\)

\(=\dfrac{5}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{101}\right)\)

\(=\dfrac{5}{2}\left(1-\dfrac{1}{101}\right)\)

\(=\dfrac{5}{2}.\dfrac{100}{101}=\dfrac{250}{101}\)

Vậy...

Adorable Angel
26 tháng 5 2017 lúc 15:02

21.3" id="MathJax-Element-7-Frame" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-table; float:none; font-size:22.5px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal; word-wrap:normal" tabindex="0"> + 23.5" id="MathJax-Element-8-Frame" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-table; float:none; font-size:22.5px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal; word-wrap:normal" tabindex="0"> + 25.7" id="MathJax-Element-9-Frame" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-table; float:none; font-size:22.5px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal; word-wrap:normal" tabindex="0"> +......+299.101" id="MathJax-Element-10-Frame" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-table; float:none; font-size:22.5px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal; word-wrap:normal" tabindex="0">

\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{101}\)

\(=1-\dfrac{1}{101}\)

\(=\dfrac{101}{101}+\dfrac{-1}{101}\)

\(=\dfrac{100}{101}\)

Dương Nguyễn
26 tháng 5 2017 lúc 15:09

21.3" id="MathJax-Element-1-Frame" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline; float:none; line-height:normal; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" tabindex="0">23.5" id="MathJax-Element-2-Frame" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline; float:none; line-height:normal; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" tabindex="0">25.7" id="MathJax-Element-3-Frame" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-table; float:none; line-height:normal; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" tabindex="0">299.101" id="MathJax-Element-4-Frame" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline; float:none; line-height:normal; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" tabindex="0">299.101

Gọi tổng của các phân số trên là A.

Ta có:

\(A=\dfrac{2}{2}.\left(\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{101}\right)\)

\(A=1.\left(\dfrac{1}{1}-\dfrac{1}{101}\right)\)

\(A=1.\dfrac{100}{101}=\dfrac{100}{101}\)

Vậy \(A=\dfrac{100}{101}.\)

b)

51.3" id="MathJax-Element-5-Frame" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline; float:none; line-height:normal; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" tabindex="0">53.5" id="MathJax-Element-6-Frame" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline; float:none; line-height:normal; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" tabindex="0">55.7" id="MathJax-Element-7-Frame" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline; float:none; line-height:normal; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" tabindex="0">599.101" id="MathJax-Element-8-Frame" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-table; float:none; line-height:normal; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" tabindex="0">599.101

Gọi tổng các phân số trên là B.

Ta có:

\(B=\dfrac{5}{2}.\left(\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{101}\right)\)

\(B=\dfrac{5}{2}.\left(\dfrac{1}{1}-\dfrac{1}{101}\right)\)

\(B=\dfrac{5}{2}.\dfrac{100}{101}\)

\(B=\dfrac{250}{101}\)

Vậy \(B=\dfrac{250}{101}\).


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