Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Bài 1:
\(A=\frac{1}{\left(1+2\right)}+\frac{1}{\left(1+2+3\right)}+\frac{1}{\left(1+2+3+4\right)}\)\(+\frac{1}{\left(1+2+3+4+5\right)}+...+\)\(\frac{1}{\left(1+2+3+...+10\right)}\)
\(A=\frac{1}{3}+\frac{1}{6}+....+\frac{1}{55}\)
\(A=2\left(\frac{1}{6}+\frac{1}{12}+....+\frac{1}{110}\right)\)
\(A=2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{10}-\frac{1}{11}\right)\)
\(A=2.\left(\frac{1}{2}-\frac{1}{11}\right)\)
\(A=\frac{9}{11}\)
Bài 2 :
2) Tử số = 11 x 13 x 15 + 3 x 3 x 3 x 11 x 13 x 15 + 5 x 5 x 5 x 11 x 13 x 15 + 9 x 9 x 9 x 11 x 13 x 15
= (1 + 3 x 3 x 3 + 5 x 5 x 5 + 9 x 9 x9) x 11 x 13 x 15 = (1+27+125+ 729) x 11 x 13 x 15
Mẫu số = 11 x 13 x 17 + 3 x 3 x 3 x 13 x 15 x 19 + 5 x 5 x 5 x 13 x 15 x 17 + 9 x 9 x 9 x 13 x 15 x 17 lớn hơn 11 x 13 x 15 + 3 x 3 x 3 x 13 x 15 x 17 + 5 x 5 x 5 x 13 x 15 x 17 + 9 x 9 x 9 x 13 x 15 x 17
= (1 + 3 x 3 x 3 + 5 x 5 x 5 + 9 x 9 x9) 13 x 15 x 17 = (1+27+125+729) x 13 x 15 x 17
\(\Rightarrow A< \frac{\left(1+27+125+729\right)\times11\times13\times15}{\left(1+27+125+729\right)\times13\times15\times17}\)
\(=\frac{11}{17}\)
\(=\frac{1111}{1717}=B\)
Vậy \(A=B\)
1)\(A=\frac{1}{3}+\frac{1}{6}+...+\frac{1}{55}=2\left(\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\right)=2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\right)=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)=2.\left(\frac{1}{2}-\frac{1}{11}\right)=\frac{9}{11}\)
2) Tử số = 11 x 13 x 15 + 3 x 3 x 3 x 11 x 13 x 15 + 5 x 5 x 5 x 11 x 13 x 15 + 9 x 9 x 9 x 11 x 13 x 15
= (1 + 3 x 3 x 3 + 5 x 5 x 5 + 9 x 9 x9) x 11 x 13 x 15 = (1+27+125+ 729) x 11 x 13 x 15
Mẫu số = 11 x 13 x 17 + 3 x 3 x 3 x 13 x 15 x 19 + 5 x 5 x 5 x 13 x 15 x 17 + 9 x 9 x 9 x 13 x 15 x 17
lớn hơn 11 x 13 x 15 + 3 x 3 x 3 x 13 x 15 x 17 + 5 x 5 x 5 x 13 x 15 x 17 + 9 x 9 x 9 x 13 x 15 x 17
= (1 + 3 x 3 x 3 + 5 x 5 x 5 + 9 x 9 x9) 13 x 15 x 17 = (1+27+125+729) x 13 x 15 x 17
=> \(A
(900-45)x45+(800+55)x55
=855x45+855x55
=855x(45+55)
=855x100
=85500
2008 x ( 0,4 - 3 :7,5 )
---------------------------
2008 x 2009
2008 x ( 0,4 - 0,4 )
----------------------------
2008 x 2009
2008 x 0 1
------------------=-----------
2008 x 2009 2009
12 x 45 + 12 x 55
= 12 x (45 + 55)
= 12 x 100
= 1200
Ủng hộ mk nha ^_-
b. 399 x 45 + 55 x 399
= 399 x ( 45 +55 )
= 399 x 100
39900
1995 x 1996 - 1991 x 1995
= 1995 x ( 1996 - 1991 )
= 1995 x 5
= 9975
\(0,25+25\%\times55+\dfrac{1}{4}\times45-\dfrac{2}{8}\)
\(=\dfrac{1}{4}+\dfrac{1}{4}\times55+\dfrac{1}{4}\times45-\dfrac{1}{4}\)
\(=\dfrac{1}{4}\times\left(1+55+45-1\right)\)
\(=\dfrac{1}{4}\times100\)
\(=25\)
\(0,25+25\%\times55+\dfrac{1}{4}\times45-\dfrac{2}{8}\)
\(=\dfrac{1}{4}+\dfrac{1}{4}\times55+\dfrac{1}{4}\times45-\dfrac{1}{4}\)
\(=\dfrac{1}{4}\times1+\dfrac{1}{4}\times55+\dfrac{1}{4}\times45-\dfrac{1}{4}\times1\)
\(=\dfrac{1}{4}+\left(1+55+45-1\right)\)
\(=\dfrac{1}{4}\times100\)
\(=0,25\times100\)
\(=25\)
\(#:)\)
45 x ( 55 + 117 ) + 55 x ( 117 - 45 )
= (45 x 55 - 45 x 55) + (45 + 55) x 117
= 0 + 100 x 117 = 11700
\(45\times\left(55+117\right)+55\times\left(117-45\right)\)
\(=45\times55+45\times117+55\times117-55\times45\)
\(=\left(45\times55-45\times55\right)+45\times117+55\times117\)
\(=45\times117+55\times117\)
\(=117\times\left(45+55\right)\)
\(=117\times100\)
\(=11700\)