Cho A = 1/1 - 1/2 + 1/3 - 1/4 + ... + 1/9 - 1/10
B = ( 1/1 + 1/2 + 1/3 + ... + 1/10 ) - 2 ( 1/2 + 1/4 + ... + 1/10 )
1/ So sánh A và B
2/ Chứng minh: A = 1/6 + 1/7 + 1/8 +1/9 + 1/10
Những câu hỏi liên quan
cho A=1/1-1/2+1/2_1/4+...+1/9-1/10
B=(1/1+1/2+1/3+...+1/10)-2.(1/2+1/4+...+1/10)a, so sánh Avaf B
b, chứng minh: A=1/6+1/7+1/8+1/9+1/10
cho A = 1/1-1/2+1/3-1/4 +1/5-1/6+1/7-1/8+1/9-1/10, B = (1/1+1/2+1/3+1/4+...+1/10)-2(1/2+1/4+...+1/10. so sánh A và B
Bài làm:
Ta có: \(A=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+\frac{1}{7}-\frac{1}{8}+\frac{1}{9}-\frac{1}{10}\)
\(A=\left(1+\frac{1}{3}+...+\frac{1}{9}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{10}\right)\)
\(A=\left[\left(1+\frac{1}{3}+...+\frac{1}{9}\right)+\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{10}\right)\right]-\left[\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{10}\right)+\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{10}\right)\right]\)
\(A=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}\right)-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{10}\right)=B\)
Vậy A = B
Cho A = \(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)
B = \(\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}\right)-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{10}\right)\)
a) So sánh A và B
b) Chứng minh A = \(\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}\)
Bài1: chứng minh rằng
1-1/2+1/3-1/4+1/5-1/6+.......-1/1996=1/996+1/997+.....+1/9996
Bài 2:tính
A=1*3*5*7*.....*99/51*52*......*100
Bài 3: Cho A = 1/6*10+1/7*9+1/8*8+1/9*7+1/10*6 chứng minh rằng A= 1/8*(1/6+1/7+1/8+1/9+1/10)
Cho A =1/1-1/2+1/3-1/4+...+1/9-1/10
Chứng minh rằng A=1/6+1/7+1/8+1/9/+1/10
\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)
\(=\left(1+\frac{1}{3}+...+\frac{1}{9}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{10}\right)\)
\(=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{9}+\frac{1}{10}-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{10}\right)\)
\(=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}-1-\frac{1}{2}-...-\frac{1}{5}\)
\(=\frac{1}{6}+\frac{1}{7}+...+\frac{1}{10}\left(đpcm\right)\)
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\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\)\(\frac{1}{10}\)
\(A=\frac{1}{1}+\frac{1}{3}+...+\frac{1}{9}-\frac{1}{2}-\frac{1}{4}-...-\frac{1}{10}\)
\(A=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{9}+\frac{1}{10}-2.\frac{1}{2}-2.\frac{1}{4}-...-2.\frac{1}{10}\)
\(A=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{9}+\frac{1}{10}-1-\frac{1}{2}-...-\frac{1}{5}\)
\(A=\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}\left(đpcm\right)\)
~~~Hok tốt~~~
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CHO A=17+1/2+2/3+4/5+5/6+4/7+3/8+2/9+1/10 và
B=1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10
cho A=1/1*2+1/3*4+...+1/9*10 va B=1/6*10+1/7*9+1/8*8+1/9*7+1/10*6 tinh A/B
Bài 7: Chứng tỏ rằng:1/2^2 + 1/3^2 + 1/4^2 + ...1/100^2 3/4Bài 8: So sánh A 20^10 + 1 / 20^10 - 1 và B 20^10 - 1 / 20^10 - 3.
Đọc tiếp
Bài 7: Chứng tỏ rằng:
1/2^2 + 1/3^2 + 1/4^2 + ...1/100^2 < 3/4
Bài 8: So sánh A= 20^10 + 1 / 20^10 - 1 và B= 20^10 - 1 / 20^10 - 3.
8:
\(A=\dfrac{20^{10}-1+2}{20^{10}-1}=1+\dfrac{2}{20^{10}-1}\)
\(B=\dfrac{20^{10}-3+2}{20^{10}-3}=1+\dfrac{2}{20^{10}-3}\)
mà 20^10-1>20^10-3
nên A<B
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Số ?2 1 + ... 6 2 + ... 8 ...+ 3 10 8 + ....3 1 + ... 6 ...+ 3 8 4 + .... 10 ...+ 34 ...+ 1 7 1 + ... 9 ...+ 1 10 6 + ...4 2 + ... 7 ...+ 2 9 ...+ 3 10 ...+ 55 ...+ 1 7 4 + .... 9 7 +.... 10 10 + ...5 3 +.... 8 ...+ 1 9 5 + ... 10 0 + .....6 ...+ 1 8 6 + ... 10 ...+ 1 1 1 + ....
Đọc tiếp
Số ?
2 = 1 + ... 6 = 2 + ... 8 = ...+ 3 10 = 8 + ....
3 = 1 + ... 6 =...+ 3 8 = 4 + .... 10 = ...+ 3
4 = ...+ 1 7 = 1 + ... 9 = ...+ 1 10 = 6 + ...
4 = 2 + ... 7 = ...+ 2 9 = ...+ 3 10 = ...+ 5
5 = ...+ 1 7 = 4 + .... 9 = 7 +.... 10 = 10 + ...
5 = 3 +.... 8 = ...+ 1 9 = 5 + ... 10 = 0 + .....
6 = ...+ 1 8 = 6 + ... 10 = ...+ 1 1 = 1 + ....
2 = 1 + 1 6 = 2 + 4 8 = 5 + 3 10 = 8 + 2
3 = 1 + 2 6 = 3 + 3 8 = 4 + 4 10 = 7 + 3
4 = 3 + 1 7 = 1 + 6 9 = 8 + 1 10 = 6 + 4
4 = 2 + 2 7 = 5 + 2 9 = 6+ 3 10 = 5 + 5
5 = 4 + 1 7 = 4 + 3 9 = 7 + 2 10 = 10 + 0
5 = 3 + 2 8 = 7 + 1 9 = 5 + 4 10 = 0 + 10
6 = 5 + 1 8 = 6 + 2 10 = 9 + 1 1 = 1 + 0
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