Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right):x=\frac{3}{1.2}+\frac{3}{2.3}+\frac{3}{3.4}+...+\frac{3}{15.16}\)
\(\left(\frac{8}{16}+\frac{4}{16}+\frac{2}{16}+\frac{1}{16}\right).\frac{1}{x}=3.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{15.16}\right)\)
\(\frac{8+4+2+1}{16}.\frac{1}{x}=3.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{15}-\frac{1}{16}\right)\)
\(\frac{15}{16}.\frac{1}{x}=3.\left(1-\frac{1}{16}\right)\)
\(\frac{15}{16}.\frac{1}{x}=3.\frac{15}{16}\)
=> \(\frac{1}{x}=3\)
=> \(x=\frac{1}{3}\)
Ta có:A: 1/1.2 +1/2.3 +1/3.4+...+1/18.19+1/19.20
=> A= 1-1/2 +1/2-1/3+1/3-1/4+...+1/18-1/19+1/19-1/20
=>A= 1-1/20=19/20
Áp dụng công thức: \(\frac{1}{n\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)
Ta có:
VT=\(x-\left(\left(1-\frac{1}{2}\right)-\left(\frac{1}{2}-\frac{1}{3}\right)-...\left(\frac{1}{98}-\frac{1}{99}\right)-\left(\frac{1}{99}-\frac{1}{100}\right)\right)\)
=\(x-\frac{1}{100}\)
Dễ dàng tìm được
\(x-\frac{1}{100}=\frac{1}{100}\)
\(x=\frac{1}{50}\)
1/1.2 + 1/2.3 + 1/3.4 + ... + 1/49.50
= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/49 - 1/50
= 1 - 1/50
= 49/50
ỦNG HỘ NHA
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)
\(=1-\frac{1}{50}=\frac{49}{50}\)
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{99.100}\)
= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{99}-\frac{1}{100}\)
= \(1-\frac{1}{100}\)
\(=\frac{99}{100}\)
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
thấy đúng thì k cho mk nha mấy bạn
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{\left(x-1\right)\times x}=\frac{15}{16}\)
\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x-1}-\frac{1}{x}=\frac{15}{16}\)
\(1-\frac{1}{x}=\frac{15}{16}\)
\(\frac{1}{x}=\frac{1}{16}\)
\(\Rightarrow x=16\)
1/2.3+1/3.4+1/4.5+...+1/380
=1/2.3+1/3.4+1/4.5+...+1/19.20
=1/2-1/3+1/3-1/4+1/4-1/5+...+1/19-1/20
=1/2-1/20
=9/20
tick nha bn cám ơn
Đúng mik cho 3 tk
\(\frac{1}{3\cdot4}+\frac{1}{4.13}+\frac{1}{13.9}+\frac{1}{9\cdot23}+...+\frac{1}{49\cdot103}\)
= \(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{13}+\frac{1}{13}-\frac{1}{9}+\frac{1}{9}-\frac{1}{23}+...+\frac{1}{49}-\frac{1}{103}\)
= \(\frac{1}{3}-\frac{1}{103}\)
= \(\frac{100}{309}\)