A.\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)
So sánh A với 1
B.\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)
So sánh B với \(\frac{1}{2}\)
Cho \(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
So sánh A với 1
A=1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100
A=1-1/100
SUY RA A<1 VÌ 1/100>0
Ta có:
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(\Rightarrow A=1-\frac{1}{100}\)
\(\Rightarrow A=\frac{99}{100}\)
Mà \(\frac{99}{100}< 1\Rightarrow A< 1\)
Vậy A < 1
\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{99\cdot100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}< 1\)
So sánh :
\(A=\frac{1}{1.2^2}+\frac{1}{2.3^2}+\frac{1}{3.4^2}+...+\frac{1}{98.99^2}+\frac{1}{99.100^2}\) và \(B=\frac{5}{12}\)
so sánh các phân số sau (ko quy đồng mẫu)
A=\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\) với 1
trình bày rõ ràng
so sánh các phân số sau (ko quy đồng mẫu)
A=\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\) với 1
trình bày rõ ràng
Ta có : \(\frac{1}{2.3}< \frac{1}{1.2}\)
\(\frac{1}{3.4}< \frac{1}{2.3}\)
\(\frac{1}{4.5}< \frac{1}{3.4}\)
...
\(\frac{1}{99.100}< \frac{1}{98.99}\)
\(\Rightarrow A< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{98.99}\)
\(A< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{98}-\frac{1}{99}\)
\(A< 1-\frac{1}{99}< 1\)
\(\Rightarrow A< 1\)
A \(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)
\(=\frac{1}{2}-\frac{1}{100}\)
\(=\frac{49}{100}\)
Vì \(\frac{49}{100}< 1\Rightarrow A< 1\)
Chúc bn hk tốt :>
mẹt xi
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
\(B=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{100.101}\)
So sánh A và B
Các bạn vào đây : ~ Marshmallow ~
Hoặc : https://olm.vn/thanhvien/cutedangyeu___
Đọc stt nhé, cảm ơn!
So sánh:
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)và \(B=\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+...+\frac{1}{100}\)
So sánh A=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{100.101}\)với 1
trên violympic phải ko, mình vừa mới giải xong nè
\(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.... +\frac{1}{100}-\frac{1}{101}\)
triệt tiêu từ từ cuối cùng còn 1 - 1/101 =100/101 = 0,99000000...ĐS: A< 1Ta có:
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{100.101}\)
\(\Rightarrow A=1-\frac{1}{2}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{100}-\frac{1}{101}\)
\(\Rightarrow A=1-\frac{1}{101}=\frac{100}{101}< 1\)
Vậy : \(A< 1\)
~ Rất vui vì giúp đc bn ~ ^_<
\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{100.101}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{100}-\frac{1}{101}\)
\(A=\left(1-\frac{1}{101}\right)+\left(-\frac{1}{2}+\frac{1}{2}\right)+...+\left(-\frac{1}{100}+\frac{1}{100}\right)\)
\(A=1-\frac{1}{101}\)
\(A=\frac{100}{101}< 1\)
=> A <1
so sánh \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{49.50}\)và \(\frac{9}{10}\)
Ta có : 1/1.2 + 1/2.3 + ... + 1/49.50
= 1-1/2+1/2-1/3 +...+1/49-1/50
= 1- 1/50
= 49/50 > 45/50 = 9/10(đpcm)
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}=?\)
Làm bậy, mà đúng
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{2.4}+...+\frac{1}{99.100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
\(\frac{1}{1.2}\)+ \(\frac{1}{2.3}\)+ \(\frac{1}{3.4}\)+ \(\frac{1}{4.5}\)+ … + \(\frac{1}{99.100}\)
= \(\frac{1}{1}\)- \(\frac{1}{2}\)+ \(\frac{1}{2}\)- \(\frac{1}{3}\)+ \(\frac{1}{3}\)-\(\frac{1}{4}\)+ \(\frac{1}{4}\)- \(\frac{1}{5}\)+ … + \(\frac{1}{99}\)- \(\frac{1}{100}\)
= \(\frac{1}{1}\)- \(\frac{1}{100}\)
= \(\frac{99}{100}\)
1/1 . 2 + 1/ 2 . 3 + 1/ 3 . 4 + ... + 1/99 . 100
= 1/1 - 1/2 + 1/2 - 1/3 + ... + 1/99 - 1/100
= 1/1 - 1/100
= 100/100 + -1/100
= 99/100
#Hoq chắc _ Baccanngon