\(\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+....+\frac{1}{1+2+3+..+59}< \frac{2}{3}\)
Những câu hỏi liên quan
\(M=\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+...+59}chứngminhM< \frac{2}{3}\)
\(CMR:\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+4+5+...+59}< \frac{2}{3}\)
\(\frac{3}{9.14}+\frac{3}{14.19}+\frac{3}{19.24}+...+\frac{3}{\left(5n-1\right).\left(5n+4\right)}< \frac{1}{15}\)
Cho \(\frac{1}{M}=\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+\frac{1}{1+...+5}+....+\frac{1}{1+2+...+59}\)Chứng minh rằng M>2/3
\(\frac{1}{M}=\frac{1}{\frac{3.4}{2}}+\frac{1}{\frac{4.5}{2}}+...+\frac{1}{\frac{59.60}{2}}\)
\(\frac{1}{M}=\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{59.60}\)
\(\frac{1}{M}=2.\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....+\frac{1}{59}-\frac{1}{60}\right)\)
\(\frac{1}{M}=\frac{2}{3}-\frac{2}{60}< \frac{2}{3}\)
-theo t đề là M chứ ko phải 1/M
Đúng 0
Bình luận (0)
\(ChoM+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+....+\frac{1}{1+2+3+4+...+59}.\)
Chứng minh rằng \(M< \frac{2}{3}\)
CHO
\(\frac{1}{M}=\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+\frac{1}{1+2+3+4+5}+...+\frac{1}{1+2+3+...+59}\)
Chứng minh rằng M>\(\frac{2}{3}\)
\(\frac{1}{M}=\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+\frac{1}{1+2+3+4+5}+...+\frac{1}{1+2+3+...+59}\)
\(\frac{1}{M}=\frac{1}{3\left(1+3\right):2}+\frac{1}{4\left(1+4\right):2}+\frac{1}{5\left(1+5\right):2}+...+\frac{1}{59\left(1+59\right):2}\)
\(\frac{1}{M}=\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+...+\frac{2}{59.60}\)
\(\frac{1}{M}=2\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{59}-\frac{1}{60}\right)\)
\(\frac{1}{M}=2\left(\frac{1}{3}-\frac{1}{60}\right)\)
\(\frac{1}{M}=\frac{1}{2}.\frac{19}{60}\)
\(\frac{1}{M}=\frac{19}{120}\)
\(M=\frac{120}{19}>\frac{2}{3}\left(đpcm\right)\)
Đúng 0
Bình luận (0)
Cho:
\(\frac{1}{m}=\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+...+59}\)
Chứng minh rằng: \(m>\frac{2}{3}\).
Ta có : \(\frac{1}{m}=\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{59.60}=2\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{59}-\frac{1}{60}\right)\)
\(=2\left(\frac{1}{3}-\frac{1}{60}\right)=\frac{19}{30}\)
\(\Rightarrow m=\frac{30}{19}>\frac{2}{3}\)
Đúng 0
Bình luận (0)
\(Tac\text{ó}:\frac{1}{m}=\frac{2}{3.4}+\frac{2}{4.5}+.....+\frac{2}{59.60}=2\left(\frac{1}{3}-\frac{1}{4}+.......+\frac{1}{59}-\frac{1}{60}\right)\)
\(=>2\left(\frac{1}{3}-\frac{1}{60}\right)=\frac{19}{30}\\ =>m=\frac{30}{19}>\frac{2}{3}\)
Đúng 0
Bình luận (0)
Chứng minh
M=\(\frac{1}{1+2+3}\)+\(\frac{1}{1+2+3+4}\)+\(\frac{1}{1+2+3+4+5}\)+.....+\(\frac{1}{1+2+3+....+59}\)<\(\frac{2}{3}\)
Cho \(M=\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+...+59}\)
Chứng minh: M<2/3
1. So sánh:a. 1 và frac{1}{2}+frac{1}{2^2}+frac{1}{2^3}+.....+frac{1}{2^{50}}b. frac{1}{3}+frac{1}{3^2}+frac{1}{3^3}+.....+frac{1}{3^{100}}với frac{1}{2}c. frac{1}{4}+frac{1}{4^2}+frac{1}{4^6}+.....frac{1}{4^{1000}}với frac{1}{3}2. Tìm x, biết:a.left(frac{2}{5}-xright):1frac{1}{3}+frac{1}{2}-4b.3-frac{1-frac{1}{2}}{1+frac{1}{x}}2frac{2}{3}c.4^x+4^{x+3}4160d.2^{x-1}+5.2^{x-2}frac{7}{32}e.frac{x-100}{24}+frac{x-98}{26}+frac{x-96}{24}3g.frac{x-1}{65}+frac{x-3}{63}+frac{x-5}{61}+frac{x-7}{59}
Đọc tiếp
1. So sánh:
a. 1 và \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+.....+\frac{1}{2^{50}}\)
b. \(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+.....+\frac{1}{3^{100}}\)với \(\frac{1}{2}\)
c. \(\frac{1}{4}+\frac{1}{4^2}+\frac{1}{4^6}+.....\frac{1}{4^{1000}}\)với \(\frac{1}{3}\)
2. Tìm x, biết:
a.\(\left(\frac{2}{5}-x\right):1\frac{1}{3}+\frac{1}{2}=-4\)
b.\(3-\frac{1-\frac{1}{2}}{1+\frac{1}{x}}=2\frac{2}{3}\)
c.\(4^x+4^{x+3}=4160\)
d.\(2^{x-1}+5.2^{x-2}=\frac{7}{32}\)
e.\(\frac{x-100}{24}+\frac{x-98}{26}+\frac{x-96}{24}=3\)
g.\(\frac{x-1}{65}+\frac{x-3}{63}+=\frac{x-5}{61}+\frac{x-7}{59}\)