Tính B= ( 1/4 - 1 ) ( 1/9 - 1 ) ( 1/16 - 1 )..... ( 1/81 - 1 ) ( 1/100 - 1 )
Tính(1/4-1).(1/9-1).(1/16-1)....(1/81-1).(1/100-1)
\(=\frac{1}{1.3}.\frac{1}{2.4}...\frac{1}{9.11}=\frac{1}{1.2.3^2...9^2.10.11}\)
tính nhanh : 1/4 + 1/9 + 1/16 + ... + 1/81 + 1/100
1/4 + 1/9 + 1/16 + ... + 1 - 1/81 + 1/100
A=(1-1/4)*(1-1/9)*(1-1/16)*....*(1-1/81)*(1-1/100)
Viết tập hợp dưới dạng tính chất đặc trưng
A=( 3; 9; 27; 81 )
B= ( 4; 16; 36; 64; 100 )
C= ( 1/2 ;1/5 ;1/9 ;1/17 )
A={x|x=3n;n\(\in\)N;\(1\le n\le4\)}
B={x|x=(2k)2;k\(\in\)N;\(1\le k\le5\)}
C={x|x=\(\frac{1}{\frac{1}{2}n^3-\frac{5}{2}n^2+7n-3}\);\(n\in N\);\(1\le n\le4\)}
Cái C tui làm bừa đấy
So sánh B = (1/4 -1) x (1/9 -1) x ( 1/16 -1) x ... x (1/81 -1) x (1/100 -1) với -11/21
( 1 phần 4 - 1 ) . ( 1 phần 9 - 1 ) . ( 1 phần 16 - 1 ) ..... ( 1 phần 81 -1 ) .( 1 phần 100 - 1 ) = ?
Làm lại đề cho:
\(\left(\frac{1}{4}-1\right)\cdot\left(\frac{1}{9}-1\right)\cdot\left(\frac{1}{16}-1\right)...\left(\frac{1}{81}-1\right)\cdot\left(\frac{1}{100}-1\right)\)
Tính nhẩm
Tính: \(S=\left(\frac{1}{4}-1\right).\left(\frac{1}{9}-1\right).\left(\frac{1}{16}-1\right).....\left(\frac{1}{81}-1\right).\left(\frac{1}{100}-1\right)\)
\(S=\left(\frac{1}{4}-1\right).\left(\frac{1}{9}-1\right).\left(\frac{1}{16}-1\right)...\left(\frac{1}{81}-1\right).\left(\frac{1}{100}-1\right)\)
\(S=\frac{-3}{4}.\frac{-8}{9}.\frac{-15}{16}........\frac{-80}{81}.\frac{-99}{100}\)
\(-S=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}......\frac{80}{81}.\frac{99}{100}\)
\(-S=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}........\frac{8.10}{9.9}.\frac{9.11}{10.10}\)
\(-S=\frac{1.3.2.4.3.5........8.10.9.11}{2.2.3.3.4.4.......9.9.10.10}\)
\(-S=\frac{\left(1.2.3......8.9\right).\left(3.4.5.......10.11\right)}{\left(2.3.4.......9.10\right).\left(2.3.4........9.10\right)}\)\(=\frac{1}{10}.\frac{11}{2}=\frac{11}{20}=>S=\frac{-11}{20}\)
Ngân Hoàng Xuân: bị 2 lần rồi, ức chế v~~~
\(\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right)\left(\frac{1}{16}-1\right).....\left(\frac{1}{81}-1\right)\left(\frac{1}{100}-1\right)\)
Tính nhanh
\(\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right)\left(\frac{1}{16}-1\right)....\left(\frac{1}{81}-1\right)\left(\frac{1}{100}-1\right)\)
\(=\frac{-3}{4}.\frac{-8}{9}.\frac{-15}{16}....\frac{-80}{81}.\frac{-99}{100}\)
\(=\left[\left(-1\right).\left(-1\right)...\left(-1\right)\left(9\text{số (-1)}\right)\right].\frac{3}{4}.\frac{8}{9}....\frac{99}{100}\)
\(=\left(-1\right).\frac{1.3}{2.2}.\frac{2.4}{3.3}....\frac{9.11}{10.10}\)
\(=-\frac{1.11}{2.10}=-\frac{11}{10}\)