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14 tháng 5 2017

Bài này hơi khó hiểu xíu. Thông cảm nha babe:v

\(B=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+\frac{1}{4}\left(1+2+3+4\right)+.......+\frac{1}{20}\left(1+2+3+....+20\right)\)

\(B=1+\left(\frac{1}{2}+1\right)+2+\left(\frac{1}{2}+2\right)+3+\left(\frac{1}{2}+3\right)+.....+10+\left(\frac{1}{2}+10\right)\)(chỗ này là nhân phân phối vô đấy!)

\(B=\left(1+2+3+....+10\right)+\left(1+2+3+...+10\right)+\left(\frac{1}{2}.10\right)\)

\(B=55+55+5=115\)

16 tháng 1 2019

\(\Rightarrow B=1+\frac{1}{2}.\frac{\left(1+2\right).2}{2}+\frac{1}{3}.\frac{\left(1+3\right).3}{2}+....+\frac{1}{20}.\frac{\left(1+20\right).20}{2}\)

\(\Rightarrow B=1+\frac{1}{2}.\frac{3.2}{2}+\frac{1}{3}.\frac{4.3}{2}+...+\frac{1}{20}.\frac{21.20}{2}\)

\(\Rightarrow B=1+\frac{1}{2}.3+\frac{4}{2}+...+\frac{21}{2}\)

\(\Rightarrow B=\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+...+\frac{21}{2}\)

\(\Rightarrow B=\frac{2+3+4+...+21}{2}=...\)

Good Clever

16 tháng 1 2019

\(B=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{20}\left(1+2+3+...+20\right)\)

\(=1+\frac{1}{2}\cdot\frac{2\cdot3}{2}+\frac{1}{3}\cdot\frac{3\cdot4}{2}+...+\frac{1}{20}\cdot\frac{20\cdot21}{2}\)

\(=\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+\frac{5}{2}+...+\frac{21}{2}\)

\(=\frac{1+2+3+....+21}{2}-\frac{1}{2}\)

\(=\frac{21\cdot22}{2}\cdot\frac{1}{2}-\frac{1}{2}\)

\(=\frac{1}{2}\left(\frac{21\cdot22}{2}-1\right)\)

\(=230\cdot\frac{1}{2}\)

4 tháng 7 2017

\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{n+1}\right)\)

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

\(=\frac{1}{n+1}\)

\(1+\frac{1}{2}.\left(1+2\right)+\frac{1}{3}.\left(1+2+3\right)...+\frac{1}{20}.\left(1+2+3+...+20\right)\)

\(=1+\frac{1}{2}.2.3:2+\frac{1}{3}.3.4:2+\frac{1}{4}.4.5:2+...+\frac{1}{20}.20.21:2\)

\(=\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+\frac{5}{2}+...+\frac{21}{2}\)

\(=\frac{2+3+4+5+...+21}{2}=115\)

29 tháng 12 2015

\(B=1+\frac{1}{2}.\frac{2.3}{2}+\frac{1}{3}.\frac{3.4}{2}+\frac{1}{4}.\frac{4.5}{2}+.....+\frac{1}{20}.\frac{20.21}{2}\)

\(B=\frac{2}{2}+\frac{2.3:2}{2}+\frac{3.4:3}{2}+.....+\frac{20.21:20}{2}\)

\(B=\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+\frac{5}{2}+....+\frac{21}{2}\)

\(B=\frac{2+3+.....+21}{2}\)

\(B=\frac{\left(2+21\right).20}{2}:2=\frac{230}{2}:2=165:2=\frac{165}{2}\)

15 tháng 2 2016

B=1+1+1/2+1+2/2+1+3/2+.....+1+(1+2+...+19)/20

B=20+1/2+2/2+3/2+...+19/2

B=20+(1+2+3+..+19)/2

B=20+190/2=115

Đảm bảo chính xác 1000000%

Ủng hộ  cho mình nhen bạn

23 tháng 1 2018

\(\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+....+\frac{1}{\sqrt{100}}>10\)