Chứng tỏ rằng:
a) \(1.3.5.........99=\frac{51}{2}.\frac{52}{2}......\frac{100}{2}\)
b)\(1-\frac{1}{2}+\frac{1}{3}-...........-\frac{1}{1990}=\frac{1}{996}+\frac{1}{997}+.......+\frac{1}{1990}\)
ĐANG CẦN GÂP
Chứng tỏ rằng
\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...-\frac{1}{1990}=\frac{1}{996}+\frac{1}{997}+...+\frac{1}{1990}\)
Giúp mình với nha
Đặt A = 1-1/2+1/3-1/4 +...+1/1989-1/1990
A= (1+1/3+1/5 +...+1/1989)- ( 1/2 + 1/4 +....+1/1990 )
A=(1+1/3+1/5 +...+1/1989) - 2(1/2+1/4+1/6+.....+1/1990)
A= (1+1/3+1/5 +...+1/1989)- (1+1/2+1/3+1/4 +...+1/995)
A= 1/996+1/997 +.....+1/1990 =VP (đpcm)
Chúc các bạn thành công :)
Có điều gì sai các bạn bẩu mình nha :)
A=
Tại sao 1/2+1/4+1/6+...+1/1990=2(1/2+1/4+1/6+...+1/1990)
Chứng tỏ rằng:
\(1-\frac{1}{2}+\frac{1}{3}-...-\frac{1}{1990}=\frac{1}{996}+\frac{1}{997}+...+\frac{1}{990}\)
Chứng minh rằng:
\(1-\frac{1}{2}+\frac{1}{3}-......-\frac{1}{1990}=\frac{1}{996}+\frac{1}{997}+.....+\frac{1}{1990}\)
1,CMR:\(1-\frac{1}{2}-\frac{1}{3}-\frac{1}{4}-...-\frac{1}{1990}=\frac{1}{996}+\frac{1}{997}+\frac{1}{1990}\)
cmr 1-\(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+.......-\frac{1}{1990}=\frac{1}{996}+\frac{1}{997}+\frac{1}{998}+.......+\frac{1}{1990}\)
xét vế trái
=(1+1/3+1/5+...+1/1989)-(1/2+1/4+...+1/1990)
=(1+1/2+1/3+1/4+...+1/1990)-2.(1/2+1/4+...+1/1990)
=(1+1/2+1/3+1/4+...+1/1990)-!1+1/2+1/3+1/4+...+1/995)
=1/996+1/997+.../1+1990
vậy 1-1/2+1/3-1/4+...-1/1990=1/996+1/997+...+1/1990
cmr 1-$\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+.......-\frac{1}{1990}=\frac{1}{996}+\frac{1}{997}+\frac{1}{998}+.......+\frac{1}{1990}$
dòng dấu = thứ 3 sửa ! thành ( nha
1,CMR:
B,\(1-\frac{1}{2}-\frac{1}{3}-\frac{1}{4}-...-\frac{1}{1990}=\frac{1}{996}+\frac{1}{997}+\frac{1}{990}\)
Chứng minh rằng:
a) \(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{199}-\frac{1}{200}\)=\(\frac{1}{101}+\frac{1}{102}+\frac{1}{103}+...+\frac{1}{200}\)
b) \(\frac{51}{2}+\frac{52}{2}+...+\frac{100}{2}=1.3.5...99\)
Đặt \(S=\frac{1}{1\cdot2}+\frac{1}{3\cdot4}+...+\frac{1}{199\cdot200}\)
\(S=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{199}-\frac{1}{200}\)
\(S=\left(1+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+...+\frac{1}{199}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{200}\right)\)
\(S=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{200}\right)-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{200}\right)\)
\(S=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{200}\right)-\left(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{100}\right)\)
\(S=\frac{1}{101}+\frac{1}{102}+...+\frac{1}{200}\)
Ta có đpcm
Bạn Trí làm sai rồi!
Đề bài không yêu cầu chứng minh như bạn
CMR
\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+....-\frac{1}{1990}=\frac{1}{996}+...+\frac{1}{1990}\)
Chứng tỏ rằng:
a) 1.3.5.....99=51/2.52/2....100/2;
b) 1-1/2+1/3-....-1/1990=1/996+1/997+...+1/1990