Tính : 5/3 + 5/3x5 + 5/5x7 + ... + 5/101x103 ai xong mik tick
Bài 1: Tính nhanh
5/3+5/3x5+5/5x7+...+5/101x103
\(\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{101.103}\)
\(=\frac{2}{5}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5,7}+...+\frac{2}{101.103}\right)\)
\(=\frac{2}{5}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{101}-\frac{1}{103}\right)\)
\(=\frac{2}{5}\left(1-\frac{1}{103}\right)\)
\(=\frac{2}{5}.\left(\frac{102}{103}\right)=\frac{204}{515}\)
Nhớ kiểm tra lại cho kl nhé
Tính bằng cách thuận tiện nhất :
a) 9+ 9/2 + 9/4 + 9/8 + ... +9/128+ 9/256
b) 5/3 + 5/3x5 + 5/5x7 + ... + 5/101x103
b ) Đặt \(A=\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{101.103}\)
\(\Rightarrow A=\frac{5}{2}\left(\frac{5}{1}-\frac{5}{3}+\frac{5}{3}-\frac{5}{5}+....+\frac{5}{101}-\frac{5}{103}\right)\)
\(\Rightarrow A=\frac{5}{2}\left(5-\frac{5}{103}\right)\)
5/1x3 + 5/3x5 + 5/5x7 + ... + 5/97x99
Ai làm nhanh và đúng mk tick cho
\(\frac{5}{1\cdot3}+\frac{5}{3\cdot5}+...+\frac{5}{97\cdot99}=\frac{5}{2}\left[\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+...+\frac{1}{97\cdot99}\right]\)
\(=\frac{5}{2}\left[\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{97}-\frac{1}{99}\right]=\frac{5}{2}\left[1-\frac{1}{99}\right]\)
\(=\frac{5}{2}\cdot\frac{98}{99}=\frac{245}{99}\)
\(=\frac{5}{2}\left(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{97\times99}\right)\)
\(=\frac{5}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\right)\)
\(=\frac{5}{2}\left(1-\frac{1}{99}\right)\)
\(=\frac{5}{2}\times\frac{98}{99}\)
\(=\frac{245}{99}\)
Tính
a. 3/(3x5) + 3/(5x7) + 3/(7x9) +... + 3/(99x101)
b. 5/(3x5) +5/(5x7) +5/(7x9) +...+ 5/(99x101)
917749738461936926399639748776398646491639394748947630373937366
trình bày bài giải tính nhanh
1/1x3+1/3x5+1/5x7+1/7x9...........1/101x103
\(\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+.+\frac{1}{101}-\frac{1}{103}\right)\)
\(\frac{1}{2}\left(1-\frac{1}{103}\right)=\frac{1}{2}\cdot\frac{100}{103}=\frac{50}{103}\)
xong r đó
Ta có:
\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{101.103}\)
\(=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{101.103}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{101}-\frac{1}{103}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{103}\right)=\frac{50}{103}\)
\(\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+...+\frac{1}{101\cdot103}\)
\(=\frac{1}{2}\cdot\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-...+\frac{1}{101}-\frac{1}{103}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{103}\right)\)
\(=\frac{1}{2}\cdot\frac{102}{103}=\frac{102}{206}\)
\(=\frac{51}{103}\)
a, 2/1x3 + 2/3x5 + 2/5x7 + 2/7x9 +...+ 9/913 x 215
b,1/1x3 + 1/3x5 + 1/5x7 + 1/7x9 + 1/213 x 215
[ Giúp mik với mấy bạn ơi ai nhanh mình sẽ tick nha TvT ]
( Toán tính nhanh nha )
sửa đề câu a và câu b nhá , mik nghĩ đề như này :
\(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{213\cdot215}\)
\(=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{213}-\frac{1}{215}\)
= \(\frac{1}{1}-\frac{1}{215}\)
\(=\frac{214}{215}\)
b, đặt \(A=\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+...+\frac{1}{213\cdot215}\)
\(A\cdot2=\frac{2}{1\cdot3}+\frac{2}{3.5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{213\cdot215}\)
\(A\cdot2=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{213}-\frac{1}{215}\)
\(A\cdot2=\frac{1}{1}-\frac{1}{215}\)
\(A\cdot2=\frac{214}{215}\)
\(A=\frac{214}{215}:2\)
\(A=\frac{107}{215}\)
@ミ★Ŧɦươйǥ★彡 cảm ơn bạn nhiều
trả lời hiền thương đề bài của bạn ấy là đúm gòi nha
5/1x3+5/3x5+5/5x7+...+5/47x49
5/1x5+5/3x5+5/5x7+.....+5/99x101
sửa đề nhé:
\(\frac{5}{1\times3}+\frac{5}{3\times5}+...+\frac{5}{99\times101}\)
\(5\times\frac{1}{2}\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+...+\frac{2}{99\times101}\right)\)
\(=\frac{5}{2}\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}\right)\)
\(=\frac{5}{2}\times\left(1-\frac{1}{101}\right)\)
\(=\frac{5}{2}\times\frac{100}{101}\)
\(=\frac{250}{101}\)
các bạn ơi giúp mình với !!!!!
Bài 1: 1+ 1/5 + 2/15 + 1/125 + 1/625 + 1/3125
Bài 2: 3/1x3 + 3/3x5 + 3/5x7 + .... + 3/99x101 + 3/101x103
MÌNH CẦN GẤP . CÁC BẠN GỬI CHO MÌNH TRƯỚC 1 GIỜ NHÉ
CẢM ƠN
2) \(\frac{3}{1\times3}+\frac{3}{3\times5}+\frac{3}{5\times7}+...+\frac{3}{99\times101}+\frac{3}{101\times103}\)
\(=\frac{3}{2}\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{101\times103}\right)\)
\(=\frac{3}{2}\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{101}-\frac{1}{103}\right)\)
\(=\frac{3}{2}\times\left(1-\frac{1}{103}\right)\)
\(=\frac{3}{2}\times\frac{101}{103}\)
\(=\frac{303}{206}\)