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\(A=\frac{7}{4}+\frac{17}{9}+\frac{31}{16}+....+\frac{4999}{2500}\)
\(A=\frac{3+4}{2^2}+\frac{8+9}{3^2}+\frac{15+16}{4^2}+....+\frac{2499+2500}{50^2}\)
\(A=\frac{\left(4-1\right)+4}{2^2}+\frac{\left(9-1\right)+9}{3^2}+\frac{\left(16-1\right)+16}{4^2}+...+\frac{\left(2500-1\right)+2500}{50^2}\)
\(A=\frac{4+4-1}{2^2} +\frac{9+9-1}{3^2}+\frac{16+16-1}{4^2}+...+\frac{2500+2500-1}{50^2}\)
\(A=\frac{2^2+2^2-1}{2^2}+\frac{3^2+3^2-1}{3^2}+\frac{4^2+4^2-1}{4^2}+...+\frac{50^2+50^2-1}{50^2}\)
\(A=\frac{2\times2^2-1}{2^2}+\frac{2\times3^2-1}{3^2}+\frac{2\times4^2-1}{4^2}+...+\frac{2\times50^2-1}{50^2}\)
\(A=\left(\frac{2\times2^2}{2^2}-\frac{1}{2^2}\right)+\left(\frac{2\times3^2}{3^2}-\frac{1}{3^2}\right)+\left(\frac{2\times4^2}{4^2}-\frac{1}{4^2}\right)+...+\left(\frac{2\times50^2}{50^2}-\frac{1}{50^2}\right)\)
\(A=\left(\frac{2\times2^2}{2^2}+\frac{2\times3^2}{3^2}+\frac{2\times4^2}{4^2}+...+\frac{2\times50^2}{50^2}\right)-\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{50^2}\right)\)
\(A=\left(2+2+2+...+2\right)-\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{50^2}\right)\)
49 số 2
\(A=98-\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{50^2}\right)\)
\(>98-\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{49\times50}\right)\)
\(=98-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\right)\)
\(=98-\left(1-\frac{1}{50}\right)\)
\(=98-1+\frac{1}{50}\)
\(=97+\frac{1}{50}>97\)
\(\Rightarrow A>97\left(ĐPCM\right)\)
Nhớ tích cho mk nha thank for watching
Ta có : 1/4=1/2*2>1/2*3
1/9=1/3*3>1/3*4
...
1/100=1/10*10>1/10*11
=>A>1/2*3+1/3*4+...+1/10*11=1/2 - 1/3+1/3 - 1/4 +...+1/10 - 1/11
=1/2 - 1/11=9/22=54/132<65/132(bạn hình như viết sai đầu bài chứ cách này đúng mà!)
a, \(\frac{3}{5}+\frac{-4}{15}=\frac{9}{15}-\frac{4}{15}=\frac{5}{15}=\frac{1}{3}\)
b, \(\frac{-1}{3}+\frac{2}{5}+\frac{2}{15}=\frac{-5}{15}+\frac{6}{15}+\frac{2}{15}=\frac{3}{15}=\frac{1}{5}\)
c, \(\frac{-3}{5}+\frac{7}{21}+\frac{-4}{5}+\frac{7}{5}=\frac{-3}{5}+\frac{1}{3}+\frac{-4}{5}+\frac{7}{5}=\left(\frac{-3}{5}+\frac{-4}{5}+\frac{7}{5}\right)+\frac{1}{3}=\frac{1}{3}\)
d, \(\frac{2}{7}+\frac{1}{9}+\frac{3}{7}+\frac{5}{9}+\frac{-5}{6}=\left(\frac{2}{7}+\frac{3}{7}\right)+\left(\frac{1}{9}+\frac{5}{9}\right)+\frac{-5}{6}=\frac{5}{7}+\frac{6}{9}+\frac{-5}{6}=\frac{90}{126}+\frac{84}{126}+\frac{-105}{126}=\frac{69}{126}=\frac{23}{42}\)
e, \(\frac{-5}{7}+\frac{3}{4}+\frac{-1}{5}+\frac{-2}{7}+\frac{1}{4}=\left(\frac{-5}{7}+\frac{-2}{7}\right)+\left(\frac{3}{4}+\frac{1}{4}\right)+\frac{-1}{5}=\left(-1\right)+1+\frac{-1}{5}=\frac{-1}{5}\)
f, \(\frac{-3}{31}+\frac{-6}{17}+\frac{1}{25}+\frac{-28}{31}+\frac{-1}{17}+\frac{-1}{5}=\left(\frac{-3}{31}+\frac{-28}{31}\right)+\left(\frac{-6}{17}+\frac{-1}{17}\right)+\left(\frac{1}{25}+\frac{-1}{5}\right)=\left(-1\right)+\frac{-7}{17}+\frac{-4}{25}=\frac{-425}{425}+\frac{-175}{425}+\frac{-68}{425}=\frac{-668}{425}\)
Chúc bn học tốt
Sắp xếp theo thứ tự tăng dần là :
a) 11 phần 72 ; 7 phần 18 ; 102 phần 72
b) 31 phần 49 ; 67 phần 97 ; 93 phần 140