3/5.7+3/7.9+...+3/201.203 tại sao =3/2.(2/5.7+2/7.9+...+2/201.203)
a)\(\frac{3}{5.7}+\frac{3}{7.9}+........+\frac{3}{201.203}\)
b)\(\frac{1}{1.2}+\frac{1}{2.3}+........+\frac{1}{99.100}\)
a ) \(\frac{3}{5.7}+\frac{3}{7.9}+...+\frac{3}{201.203}\)
\(=\frac{3}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{201.203}\right)\)
\(=\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{201}-\frac{1}{203}\right)\)
\(=\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{203}\right)\)
\(=\frac{3}{2}.\left(\frac{203}{1015}-\frac{5}{1015}\right)\)
\(=\frac{3}{2}.\frac{198}{1015}\)
\(=\frac{297}{1015}\)
b ) \(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
Tham khảo nha !!!
Tính:
a) M=2/3.5+2/5.7+2/7.9+...+2/97.99
b) N=3/5.7+3/7.9+3/9.11+...+3/197.199
a.
\(M=1.\left[\frac{1}{3}-\frac{1}{5}+.....\frac{1}{97}-\frac{1}{99}\right]\)
\(M=\frac{1}{3}-\frac{1}{99}=\frac{32}{99}\)
b.
\(N=\frac{3}{2}.\left[\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{197}-\frac{1}{199}\right]\)
\(N=\frac{3}{2}.\left[\frac{1}{5}-\frac{1}{199}\right]=\frac{291}{995}\)
mk đầu tiên nha bạn
a) M = 2/3.5 + 2/5.7 + 2/7.9 + ... + 2/97.99
b) N = 3/5.7 + 3/7.9 + 3/9.11 + ... + 3/197.199
c) P = 1/1.2 + 2/2.4 + 3/4.7 + ... + 10/46.56
Tính nhanh :
\(\frac{1}{3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{201.203}\)
\(2A=\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+...+\frac{2}{201\cdot203}\)
\(2A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{201}-\frac{1}{203}\)
\(2A=1-\frac{1}{203}\)
\(A=\frac{101}{203}\)
1.3+3.5+5.7+...+201.203
6A=1.3.6 + 3.5.6 + 5.7.6 + ... + 201.203.6
6A=1.3(5+1) + 3.5(7-1) + 5.7(9-3) + ... + 201.203(205-199)
6A=(1.3.5 + 1.3) +( 3.5.7 - 1.3.5) + (5.7.9 - 3.5.7) + ... + (201.203.205 - 199.201.203)
6A=3+201.203.205
6A=8364618
A=\(\frac{8364618}{6}\)
A=1394103
máy tính cũng phải hỏng với phét tính này
Tìm x:3/3.5+3/5.7+3/7.9+...+x.(x+2)=8/9
tính biểu thức này như thế nào các thầy ơi
+
+
+……+
=
2^3/3.5 + 2^3/5.7 + 2^3/7.9 + ....... + 2^3/101.103
\(\dfrac{2^3}{3\cdot5}+\dfrac{2^3}{5\cdot7}+...+\dfrac{2^3}{101\cdot103}\)
\(=2^2\left(\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+...+\dfrac{2}{101\cdot103}\right)\)
\(=4\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{101}-\dfrac{1}{103}\right)\)
\(=4\cdot\left(\dfrac{1}{3}-\dfrac{1}{103}\right)\)
\(=4\cdot\dfrac{100}{309}=\dfrac{400}{309}\)
\(B=\frac{2^3}{3.5}+\frac{2^3}{5.7}+\frac{2^3}{7.9}+......+\frac{2^3}{101.103}\)
\(B=\frac{2^3}{3.5}+\frac{2^3}{5.7}+....+\frac{2^3}{101.103}\)
\(\Rightarrow\frac{1}{2^2}.B=\frac{2}{3.5}+\frac{2}{4.7}+....+\frac{2}{101.103}\)
\(\Rightarrow\frac{1}{4}.B=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{101}-\frac{1}{103}\)
\(\Rightarrow\frac{1}{4}.B=\frac{1}{3}-\frac{1}{103}=\frac{100}{309}\)
\(\Rightarrow B=\frac{100}{309}:\frac{1}{4}=\frac{400}{309}\)
\(=2^2\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{101.103}\right)\)
\(=4\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{101}-\frac{1}{103}\right)\)
\(=4\left(\frac{1}{3}-\frac{1}{103}\right)\)
\(=4\cdot\frac{100}{309}=\frac{400}{309}\)
bài 3 tính tổng
a, A=2/3.5+2/5.7+2/7.9+.....+2/201.203
b, B=3/4.7+3/7.10+3/10.13+.....+3/73.76
mik đang gấp lắm
a: \(A=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{201}-\dfrac{1}{203}=\dfrac{1}{3}-\dfrac{1}{203}=\dfrac{200}{609}\)
b: \(B=\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{73}-\dfrac{1}{76}\)
\(=\dfrac{1}{4}-\dfrac{1}{76}=\dfrac{18}{76}=\dfrac{9}{38}\)