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2 tháng 3 2019

M= 1 + 1/2.3 + 1/3.6 + 1/4.10 +.....+ 1/16.136
M=1 + 3/2 + 2 + 5/2 +...+ 17/2
M= 2/2 + 3/2 + 4/2 + 5/2 +...+ 17/2
M=\(\frac{2+3+4+5+...+17}{2}\)

M= 152/2=76

1 tháng 11 2016

\(=1+\frac{3}{2}+2+\frac{5}{2}+3+\frac{7}{2}+...+8+\frac{17}{2}\)

\(=\left(1+2+...+8\right)+\left(\frac{3}{2}+\frac{5}{2}+...+\frac{17}{2}\right)=36+\frac{80}{2}=36+40=76\)

1 tháng 11 2016

\(B=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+\frac{1}{4}\left(1+2+3+4\right)+...+\frac{1}{16}.\left(1+2+3+...+16\right)\)

\(B=1+\frac{1}{2}.\frac{\left(1+2\right).2}{2}+\frac{1}{3}.\frac{\left(1+3\right).3}{2}+\frac{1}{4}.\frac{\left(1+4\right).4}{2}+...+\frac{1}{16}.\frac{\left(1+16\right).16}{2}\)

\(B=1+\frac{1}{2}.\frac{3.2}{2}+\frac{1}{3}.\frac{4.3}{2}+\frac{1}{4}.\frac{5.4}{2}+...+\frac{1}{16}.\frac{17.16}{2}\)

\(B=1+\frac{3}{2}+\frac{4}{2}+\frac{5}{2}+...+\frac{17}{2}\)

\(B=\frac{1}{2}.\left(2+3+4+5+...+17\right)\)

\(B=\frac{1}{2}.\frac{\left(2+17\right).16}{2}=19.4=76\)

3 tháng 12 2016

Đặt \(A=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+\frac{1}{4}\left(1+2+3+4\right)+...+\frac{1}{16}\left(1+2+3+...+16\right)\)

\(A=1+\frac{1+2}{2}+\frac{1+2+3}{3}+\frac{1+2+3+4}{4}+...+\frac{1+2+3+...+16}{16}\)

\(A=1+\frac{2\left(2+1\right):2}{2}+\frac{3\left(3+1\right):2}{3}+\frac{4\left(4+1\right):2}{4}+...+\frac{16\left(16+1\right):2}{16}\)

\(A=1+\frac{2+1}{2}+\frac{3+1}{2}+\frac{4+1}{2}+...+\frac{16+1}{2}\)

\(A=\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+\frac{5}{2}+...+\frac{17}{2}\)

\(A=\frac{2+3+4+5+...+17}{2}\)

\(A=\frac{152}{2}\)

\(A=76\)

 

A=1+\(\frac{1+2}{2}\)+\(\frac{1+2+3}{3}\)+...+\(\frac{1+2+3+...+16}{16}\)

A=\(\frac{2}{2}\)+\(\frac{3}{2}\)+\(\frac{4}{2}\)+...+\(\frac{17}{2}\)

A=\(\frac{2+3+4+...+17}{2}\)

A=76(đề thi HSG huyện tui có tui làm zậy mà cũng có điểm tuyệt đối)

4 tháng 5 2016

\(A=1+\frac{1}{2}.\left(1+2\right)+\frac{1}{3}.\left(1+2+3\right)+....+\frac{1}{16}.\left(1+2+3+....+16\right)\)

\(A=1+\frac{1}{2}\cdot\frac{2.3}{2}+\frac{1}{3}\cdot\frac{3.4}{2}+\frac{1}{4}\cdot\frac{4.5}{2}+.....+\frac{1}{16}\cdot\frac{16.17}{2}\)

\(A=\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+....+\frac{17}{2}\)

\(A=\frac{\left(2+3+4+.....+17\right)}{2}=\frac{\left(2+17\right).16}{2}=\frac{152}{2}=76\)

13 tháng 9 2018

A = 1 + 1/2.(1+2) + 1/3.(1+2+3) + 1/4.(1+2+3+4) + ...+ 1/16.(1+2+....+16)

A = 1 + 1/2.3 + 1/3.6 + 1/4.10 + ...+ 1/16.136

A = 1 + 3/2 + 4/2 + 5/2 + ....+ 17/2

A = 1 + (3+4+5+...+17)/2

A = 1 + 150/2

A = 1 + 75

A = 76

13 tháng 9 2018

A = 1 + 1/2.(1+2) + 1/3.(1+2+3) + 1/4.(1+2+3+4) + ...+ 1/16.(1+2+....+16)

A = 1 + 1/2.3 + 1/3.6 + 1/4.10 + ...+ 1/16.136

A = 1 + 3/2 + 4/2 + 5/2 + ....+ 17/2

A = 1 + (3+4+5+...+17)/2

A = 1 + 150/2

A = 1 + 75

A = 76

4 tháng 7 2019

\(\frac{\frac{1}{3}+\frac{1}{7}-\frac{1}{17}}{\frac{2}{3}+\frac{2}{7}-\frac{2}{17}}.\frac{\frac{3}{4}-\frac{3}{16}+\frac{3}{256}-\frac{3}{4}}{1-\frac{1}{4}+\frac{1}{16}-\frac{1}{64}}-\frac{-5}{8}\)

\(\frac{1.\left(\frac{1}{3}+\frac{1}{7}-\frac{1}{17}\right)}{2.\left(\frac{1}{3}+\frac{1}{7}-\frac{1}{17}\right)}.\frac{3.\left(\frac{1}{4}-\frac{1}{16}-\frac{1}{256}+\frac{1}{4}\right)}{1-\frac{1}{4}+\frac{1}{16}-\frac{1}{64}}+\frac{5}{8}\)

\(\frac{1}{2}.\left(\frac{3.\left(\frac{3}{4}+\frac{63}{256}\right)}{\frac{3}{4}+\frac{3}{64}}\right)+\frac{5}{8}\)

\(\frac{1}{2}.\left(\frac{3.\left(\frac{3}{4}+\frac{63}{256}\right)}{\frac{3}{4}+\frac{12}{256}}\right)+\frac{5}{8}\)

\(\frac{1}{2}.\left(\frac{3.3.\left(\frac{1}{4}+\frac{21}{256}\right)}{3.\left(\frac{1}{4}+\frac{1}{64}\right)}\right)+\frac{5}{8}\)

\(\frac{1}{2}.\left(\frac{3.\left(\frac{1}{4}+\frac{1}{64}+\frac{17}{256}\right)}{\frac{1}{4}+\frac{1}{64}}\right)+\frac{5}{8}\)

\(\frac{1}{2}.\left(\frac{3.\left(\frac{1}{4}+\frac{1}{64}\right)+3.\frac{17}{256}:\left(\frac{1}{4}+\frac{1}{64}\right)}{1.\left(\frac{1}{4}+\frac{1}{64}\right)}\right)+\frac{5}{8}\)

\(\frac{1}{2}.\left(3+\frac{51}{256}:\frac{17}{64}\right)+\frac{5}{8}\) 

\(\frac{1}{2}.\left(3+\frac{3}{4}\right)+\frac{5}{8}\)

\(\frac{1}{2}.\frac{15}{4}+\frac{5}{8}\)

\(\frac{15}{8}+\frac{5}{8}\)

\(\frac{5}{2}\)

4 tháng 7 2019

\(\frac{\frac{1}{3}+\frac{1}{7}-\frac{1}{17}}{\frac{2}{3}+\frac{2}{7}-\frac{2}{17}}.\frac{\frac{3}{4}-\frac{3}{16}-\frac{3}{256}+\frac{3}{4}}{1-\frac{1}{4}+\frac{1}{16}-\frac{1}{64}}-\frac{-5}{8}\)

\(=\frac{\frac{1}{3}+\frac{1}{7}-\frac{1}{17}}{2.\left(\frac{1}{3}+\frac{1}{7}-\frac{1}{17}\right)}.\frac{\frac{3}{4}-\frac{3}{16}-\frac{3}{256}+\frac{3}{4}}{1-\frac{1}{4}+\frac{1}{16}-\frac{1}{64}}+\frac{5}{8}\)

\(=\frac{1}{2}.\frac{111}{68}+\frac{5}{8}\)

\(=\frac{49}{34}\)