tính theo cách hợp lí
a) $$
b) \(\frac{1}{2}-\frac{1}{2016.2015}-\frac{1}{2015.2014}-....-\frac{1}{3.2}\)
tính theo cách hợp lí
a) \(\frac{3}{1.3}+\frac{3}{3.5}+.....+\frac{3}{49.51}\)
b) \(\frac{1}{2}-\frac{1}{2016.2015}-\frac{1}{2015.2014}-....-\frac{1}{3.2}\)
tính
\(\frac{1}{2}-\frac{1}{2016.2015}-\frac{1}{2015.2014}-...-\frac{1}{3.2}\)
\(\frac{1}{2}-\frac{1}{2016.2015}-\frac{1}{2015.2014}-...-\frac{1}{3.2}\)
\(=\frac{1}{2}-\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2015.2016}\right)\)
\(=\frac{1}{2}-\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2015}-\frac{1}{2016}\right)\)
\(=\frac{1}{2}-\left(\frac{1}{2}-\frac{1}{2016}\right)\)
\(=\frac{1}{2}-\frac{1}{2}+\frac{1}{2016}\)
\(=\frac{1}{2016}\)
\(\frac{1}{2}-\frac{1}{2016.2015}-\frac{1}{2015.2014}-...-\frac{1}{3.2}\)
\(=\frac{1}{2}-\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2014.2015}+\frac{1}{2015.2016}\right)\)
\(=\frac{1}{2}-\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2015}-\frac{1}{2016}\right)\)
\(=\frac{1}{2}-\left(\frac{1}{2}-\frac{1}{2016}\right)\)
\(=\frac{1}{2}-\frac{1}{2}+\frac{1}{2016}\)
\(=0+\frac{1}{2016}=\frac{1}{2016}\)
\(\frac{1}{2017.2016}\)-\(\frac{1}{2016.2015}\)-\(\frac{1}{2015.2014}\)-...................-\(\frac{1}{3.2}\)-\(\frac{1}{2.1}\)
Bài 3 : Tính :
A = \(\frac{1}{2016.2015}+\frac{1}{2015.2014}+\frac{1}{2014.2013}+....+\frac{1}{1.2}\)
\(A=\frac{1}{2016.2015}+\frac{1}{2015.2014}+\frac{1}{2014.2013}+...+\frac{1}{1.2}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2014}-\frac{1}{2015}+\frac{1}{2015}-\frac{1}{2016}\)
\(=1-\frac{1}{2016}=\frac{2015}{2016}\)
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
= 2015/2016 nha bạn
Tính nhanh:
a)\(A=\frac{1}{2015}-\frac{1}{2015.2014}-\frac{1}{2014.2013}-...-\)\(\frac{1}{3.2}-\frac{1}{2.1}\)
b)\(B=54-\frac{1}{2}.\left(1+2\right)-\frac{1}{3}.\left(1+2+3\right)\)\(-...-\frac{1}{12}.\left(1+2+3+..+12\right)\)
Giải Hộ Mình Pls
A=1/2015-1/2015.2014-....-1/3.2-1/2.1
A=1/2015-[1/2015.2014+1/2014.2013+....+1/3.2+1/2.1]
A=1/2015-[1/1.2+1/2.3+....1/2014.2015]
A=1/2015-[1-1/2+1/2-1/3+...+1/2014-1/2015]
A=1/2015-[1-2015]
A=1/2015-1+1/2015
A=[1/2015+1/2015]-1
A=2/2015-1
A=-2013/2015
\(\frac{1}{2016.2015}\) + \(\frac{1}{2015.2014}\) + \(\frac{1}{2013.2014}\) + ... + \(\frac{1}{1.2}\)
bai nay ban viet nguoc day so lai roi giai nhu binh thuong la duoc
-1/2016.2015-1/2015.2014-1/2013.2012-...-1/3.2-1/2.1
=\(-\frac{1}{2016}+\frac{1}{2015}-\frac{1}{2015}+\frac{1}{2014}-...-\frac{1}{2}+1\)
=\(-\frac{1}{2016}+1=\frac{2015}{2016}\)
Ta có :\(\frac{-1}{2016.2015}-\frac{1}{2015.2014}-\frac{1}{2014.2013}-...-\frac{1}{3.2}-\frac{1}{2.1}\)
= \(-\left(\frac{1}{2016.2015}+\frac{1}{2015.2014}+\frac{1}{2014.2013}+...+\frac{1}{3.2}+\frac{1}{2.1}\right)\)
= \(-\left(\frac{1}{2016}-\frac{1}{2015}+\frac{1}{2015}-\frac{1}{2014}+\frac{1}{2014}-\frac{1}{2013}+...+\frac{1}{3}-\frac{1}{2}+\frac{1}{2}-\frac{1}{1}\right)\)
= \(-\left(\frac{1}{2016}-1\right)\)
= \(-\left(-\frac{2015}{2016}\right)\)
= \(-\frac{2015}{2016}\)
Mk làm kĩ lắm rồi. ko tích nữa mk cũng chịu bạn luôn @@
Bài 2: Thực hiện các phép tính sau một cách hợp lý:\(D=\frac{1}{99}-\frac{1}{99.98}-\frac{1}{98.97}-\frac{1}{97.96}-....-\frac{1}{3.2}-\frac{1}{2.1}\)
D =1/99 -1/99.98-1/98.97-...-1/3.2-1/2.1
=1/99-(1/99.98+1/98.97-...-1/3.2+1/2.1)
=1/99-(1/1.2+1/2.3+1/3.4+...+1/98.99)
=1/99-(1/1-1/2+1/2-1/3+1/3-1/4+1/4-...+1/98-1/99)
=1/99-(1/1-1/99)
=1/99-98/99
=-97/99
Bạn tham khảo :
Lấy bài tại link : https://olm.vn/hoi-dap/detail/243536225427.html
#Duongw
\(D=\frac{1}{99}-\frac{1}{99.98}-\frac{1}{98.97}-...-\frac{1}{3.2}-\frac{1}{2.1}\)
\(D=\frac{1}{99}-\left(\frac{1}{99.98}+\frac{1}{98.97}+...+\frac{1}{3.2}+\frac{1}{2.1}\right)\)
\(D=\frac{1}{99}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}\right)\)
\(D=\frac{1}{99}-\frac{98}{99}=-\frac{97}{99}\)
Tính : \(\frac{1}{2015.2014}-\frac{1}{2014.2013}-\frac{1}{2013.2012}-...-\frac{1}{2}\)
\(=\frac{2015-2014}{2015.2014}-\frac{2014-2013}{2014.2013}-\frac{2013-2012}{2013.2012}-...-\frac{2-1}{2.1}\)
\(=\left(\frac{2015}{2015.2014}-\frac{2014}{2015.2014}\right)-\left(\frac{2014}{2014.2013}-\frac{2013}{2014.2013}\right)-...-\left(\frac{2}{2.1}-\frac{1}{2.1}\right)\)
\(=\left(\frac{1}{2014}-\frac{1}{2015}\right)-\left(\frac{1}{2013}-\frac{1}{2014}\right)-\left(\frac{1}{2012}-\frac{1}{2013}\right)-...-\left(1-\frac{1}{2}\right)\)
\(=\frac{1}{2014}-\frac{1}{2015}-\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2012}+\frac{1}{2013}-...-1+\frac{1}{2}\)
\(=\frac{1}{2014}-\frac{1}{2015}+\frac{1}{2014}-1=\frac{1}{1007}-\frac{1}{2015}-1=...\)