Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(\frac{1}{2}-\frac{1}{2016.2015}-\frac{1}{2015.2014}-...-\frac{1}{3.2}\)
\(=\frac{1}{2}-\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2015.2016}\right)\)
\(=\frac{1}{2}-\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2015}-\frac{1}{2016}\right)\)
\(=\frac{1}{2}-\left(\frac{1}{2}-\frac{1}{2016}\right)\)
\(=\frac{1}{2}-\frac{1}{2}+\frac{1}{2016}\)
\(=\frac{1}{2016}\)
\(\frac{1}{2}-\frac{1}{2016.2015}-\frac{1}{2015.2014}-...-\frac{1}{3.2}\)
\(=\frac{1}{2}-\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2014.2015}+\frac{1}{2015.2016}\right)\)
\(=\frac{1}{2}-\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2015}-\frac{1}{2016}\right)\)
\(=\frac{1}{2}-\left(\frac{1}{2}-\frac{1}{2016}\right)\)
\(=\frac{1}{2}-\frac{1}{2}+\frac{1}{2016}\)
\(=0+\frac{1}{2016}=\frac{1}{2016}\)
\(=\frac{2015-2014}{2015.2014}-\frac{2014-2013}{2014.2013}-\frac{2013-2012}{2013.2012}-...-\frac{2-1}{2.1}\)
\(=\left(\frac{2015}{2015.2014}-\frac{2014}{2015.2014}\right)-\left(\frac{2014}{2014.2013}-\frac{2013}{2014.2013}\right)-...-\left(\frac{2}{2.1}-\frac{1}{2.1}\right)\)
\(=\left(\frac{1}{2014}-\frac{1}{2015}\right)-\left(\frac{1}{2013}-\frac{1}{2014}\right)-\left(\frac{1}{2012}-\frac{1}{2013}\right)-...-\left(1-\frac{1}{2}\right)\)
\(=\frac{1}{2014}-\frac{1}{2015}-\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2012}+\frac{1}{2013}-...-1+\frac{1}{2}\)
\(=\frac{1}{2014}-\frac{1}{2015}+\frac{1}{2014}-1=\frac{1}{1007}-\frac{1}{2015}-1=...\)
bai nay ban viet nguoc day so lai roi giai nhu binh thuong la duoc
b: \(=\dfrac{1}{2}-\left(\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2015}-\dfrac{1}{2016}\right)\)
\(=\dfrac{1}{2}-\dfrac{1}{2}+\dfrac{1}{2016}=\dfrac{1}{2016}\)
5/4:1/4:(11/6-3/2)+1
5/4:1/4:1/3+1
5/4.4/1:1/3+1
5/4.4/1.3/1+1
5.1/3+1
5/3+1
5/3+1/1
5/3+3/3
8/3
\(125\%.\left(-\frac{1}{2}\right)^2:\left(1\frac{5}{6}-1,5\right)\)
\(=\frac{5}{4}.\left(-\frac{1}{2}\right)^2:\left(\frac{11}{6}-1,5\right)\)
\(=\frac{5}{4}.\frac{1}{4}:\left(\frac{11}{6}-\frac{3}{2}\right)\)
\(=\frac{5}{4}.\frac{1}{4}:\frac{1}{3}\)
\(=\frac{5}{4}:\frac{3}{4}=\frac{5}{3}\)
b, \(|\frac{2}{3}x-\frac{1}{2}|=\frac{5}{6}\)
\(\frac{2}{3}x-\frac{1}{2}=\frac{5}{6}\)hoặc\(-\frac{5}{6}\)
\(\frac{2}{3x}=\frac{5}{6}+\frac{1}{2}\)hoặc \(\frac{2}{3}x=-\frac{5}{6}+\frac{1}{2}\)
\(\frac{2}{3}x=\frac{4}{3}\)hoặc \(-\frac{1}{3}\)
\(x=\frac{4}{3}:\frac{2}{3}\)hoặc \(-\frac{1}{3}:\frac{2}{3}\)
\(x=2\)hoặc \(-\frac{1}{2}\)
Bài 2:
\(=\frac{2017}{2016}\)
Bài 3 :
O x y z t
a, trên cùng một nửa mặt phẳng bờ chứa tia Ox, tia Oz nằm giữa 2 tia còn lại . Vì \(\widehat{xOz}< \widehat{xOy}\left(100< 50\right)\)
b, Vì tia Oz nằm giữa 2 tia còn lại nên ta có :
\(\widehat{yOz}+\widehat{zOx}=\widehat{xOy}\)
\(\widehat{yOz}+50=100\)
\(\widehat{yOz}=100-50=50\)
Vậy tia Oz là tia phân giác của góc \(\widehat{xOy}\).Vì tia Oz nằm giữa 2 tia còn lại và 2 góc yOz và zOx bằng nhau = 50
c, Vì tia Ot là tia đối của Ox nên có số đo là 180 nên \(\Rightarrow\)\(\widehat{xOt}=180\)
\(B=\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{9.10}\)
\(B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....++\frac{1}{9}-\frac{1}{10}\)
\(B=1-\frac{1}{10}=\frac{9}{10}\)
\(C=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)
\(C=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
\(C=1-\frac{1}{100}\)
\(C=\frac{99}{100}\)
a ) \(\frac{4}{20}+\frac{16}{42}+\frac{6}{15}+\frac{-3}{5}+\frac{2}{21}+\frac{-10}{21}+\frac{3}{20}\)
\(=\frac{4}{20}+\frac{8}{21}+\frac{2}{5}-\frac{3}{5}+\frac{2}{21}+\frac{-10}{21}+\frac{3}{20}\)
\(=\left(\frac{4}{20}+\frac{3}{20}\right)+\left(\frac{8}{21}+\frac{2}{21}-\frac{10}{21}\right)+\left(\frac{2}{5}-\frac{3}{5}\right)\)
\(=\frac{7}{20}+0+\frac{-1}{5}=\frac{7-4}{20}=\frac{3}{20}\)
b ) \(\frac{42}{46}+\frac{250}{186}+\frac{-2121}{2323}+\frac{-125125}{143143}\)
\(=\frac{21}{23}+\frac{-21}{23}+\frac{-125}{143}\)
\(=0+\frac{-125}{143}=-\frac{125}{143}\)
bài 2
a \(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2003.2004}\)
=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2003}-\frac{1}{2004}\)
=\(1-\frac{1}{2004}=\frac{2003}{2004}\)
Bài 1 mik học xong quên hết òi (mấy bài kia là hok biết luôn :V)
\(A=\frac{1}{2016.2015}+\frac{1}{2015.2014}+\frac{1}{2014.2013}+...+\frac{1}{1.2}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2014}-\frac{1}{2015}+\frac{1}{2015}-\frac{1}{2016}\)
\(=1-\frac{1}{2016}=\frac{2015}{2016}\)
Vậy \(A=\frac{2015}{2016}\).
Mình viết ngược lại cho dễ làm xD
\(A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{2014\cdot2015}+\frac{1}{2015\cdot2016}\)
\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2015}-\frac{1}{2016}\)
\(A=\frac{1}{1}-\frac{1}{2016}\)
\(A=\frac{2015}{2016}\)
Sai thì bỏ quá :3