Bạn phân tích ra từng bước
So sánh \(\frac{2}{5}< S< \frac{8}{9}\)
~~~~~~~~~~ Chúc bạn học tốt ~~~~~~~~~~~
Bạn phân tích ra từng bước
Rồi đi so sánh
~~~~~~~ Chúc bạn học tốt ~~~~~~~
1/2.2 = 1/2.2 > 1/2.3
1/3.2 = 1/3.3 > 1/3.4
1/4.2 = 1/4.4 > 1/4.5
1/5.2 = 1/5.5 > 1/5.6
1/6.2 = 1/6.6 > 1/6.7
1/7.2 = 1/7.7 > 1/7.8
1/8.2 = 1/8.8 > 1/8.9
1/9.2 = 1/9.9 > 1/9.10
=> S = 1/ 2.2 + 1/3.2 + 1/4.2 + …..+ 1/9.2 > 1/2.3 + 1/3.4 + 1/4.5…...+ 1/9.10
=> S > 1/2.3 + 1/3.4 + 1/4.5…...+ 1/9.10
=> S > 1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5…...+ 1/9 – 1/10
=> S > 1/2 – 1/10
=> S > 1.5/2.5 – 1/10
=> S > 4/10
=> S > 2/5
Tương tự ta có:
1/2.2 = 1/2.2 < 1/1.2
1/3.2 = 1/3.3 < 1/2.3
1/4.2 = 1/4.4 < 1/3.4
1/5.2 = 1/5.5 < 1/4.5
1/6.2 = 1/6.6 < 1/5.6
1/7.2 = 1/7.7 < 1/6.7
1/8.2 = 1/8.8 < 1/7.8
1/9.2 = 1/9.9 < 1/8.9
=> S = 1/ 2.2 + 1/3.2 + 1/4.2 + …..+ 1/9.2 < 1/1.2 + 1/2.3 + 1/3.4 + …...+ 1/8.9
=> S < 1/1.2 + 1/2.3 + 1/3.4 + …...+ 1/8.9
=> S < 1/1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + …...+ 1/8 – 1/9
=> S < 1/1 – 1/9
=> S < 1/1 – 1/9
=> S < 8/9
Vậy \(\frac{2}{5}< S< \frac{8}{9}\)
phân tích ra nha bạn yêu <3
so sánh 2/5 < S < 8/9 nha bạn ~
ta có:1/2.3<1/22<1/1.2
làm như vậy đến 1/9.10<1/92<1/8.9
suy ra 1/2.3+1/3.4+...+1/9.10<S<1/1.2+1/2.3+1/3.4+...+1/8.9
suy ra1/2-1/3+1/3-1/4+...+1/9-1/10<S<1-1/2+1/2-1/3+1/3-1/4+.....+1/8-1/9
suy ra1/2-1/10<S<1-1/9 suy ra4/5<S<8/9
mà 2/5<4/5
suy ra 2/5<S<8/9(đpcm)
Ta có:
\(\frac{1}{2^2}>\frac{1}{2.3};\frac{1}{3^2}>\frac{1}{3.4};...;\frac{1}{9^2}>\frac{1}{9.10}\)
\(=>S>\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\)
\(=>S>\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)
\(=>S>\frac{1}{2}-\frac{1}{10}\)
\(=>S>\frac{2}{5}\)*
Ta lại có:
\(\frac{1}{2^2}< \frac{1}{1.2};\frac{1}{3^2}< \frac{1}{2.3};...;\frac{1}{9^2}< \frac{1}{8.9}\)
\(=>S< \frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{8.9}\)
\(=>S< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{8}-\frac{1}{9}\)
\(=>S< 1-\frac{1}{9}\)
\(=>S< \frac{8}{9}\)**
Từ * và ** \(=>\frac{2}{5}< S< \frac{8}{9}\)
\(S=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{9^2}\)
\(\Rightarrow S>\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\)
\(\Rightarrow S>\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)
\(\Rightarrow S>\frac{1}{2}-\frac{1}{10}\)
\(\Rightarrow S>\frac{2}{5}\)
tương tự ta có:
\(S=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{9^2}\)
\(\Rightarrow S< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{8.9}\)
\(\Rightarrow S< \frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}\)
\(\Rightarrow S< 1-\frac{1}{9}\)
\(\Rightarrow S< \frac{8}{9}\)
vậy\(\frac{2}{5}< S< \frac{8}{9}\)
1/2.2 = 1/2.2 > 1/2.3
1/3.2 = 1/3.3 > 1/3.4
1/4.2 = 1/4.4 > 1/4.5
1/5.2 = 1/5.5 > 1/5.6
1/6.2 = 1/6.6 > 1/6.7
1/7.2 = 1/7.7 > 1/7.8
1/8.2 = 1/8.8 > 1/8.9
1/9.2 = 1/9.9 > 1/9.10
=> S = 1/ 2.2 + 1/3.2 + 1/4.2 + …..+ 1/9.2 > 1/2.3 + 1/3.4 + 1/4.5…...+ 1/9.10
=> S > 1/2.3 + 1/3.4 + 1/4.5…...+ 1/9.10
=> S > 1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5…...+ 1/9 – 1/10
=> S > 1/2 – 1/10
=> S > 1.5/2.5 – 1/10
=> S > 4/10
=> S > 2/5
Tương tự ta có:
1/2.2 = 1/2.2 < 1/1.2
1/3.2 = 1/3.3 < 1/2.3
1/4.2 = 1/4.4 < 1/3.4
1/5.2 = 1/5.5 < 1/4.5
1/6.2 = 1/6.6 < 1/5.6
1/7.2 = 1/7.7 < 1/6.7
1/8.2 = 1/8.8 < 1/7.8
1/9.2 = 1/9.9 < 1/8.9
=> S = 1/ 2.2 + 1/3.2 + 1/4.2 + …..+ 1/9.2 < 1/1.2 + 1/2.3 + 1/3.4 + …...+ 1/8.9
=> S < 1/1.2 + 1/2.3 + 1/3.4 + …...+ 1/8.9
=> S < 1/1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + …...+ 1/8 – 1/9
=> S < 1/1 – 1/9
=> S < 1/1 – 1/9
=> S < 8/9
Vậy 25 <S<89
Để làm được bài này
-Phân tích các số
Ví dụ; Phân tích các số \(\frac{1}{2^2^{ }}+\frac{1}{3^2}+\frac{1}{4^2}......+\frac{1}{9^2}\)
Rồi ta sẽ đi so sánh các số
Vậy ta có KQ là
\(\frac{2}{5}< S< \frac{8}{9}\)
MAGICPENCIL
HÃY LUÔN :-)
