Tính B biết :
\(B=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+\frac{1}{4}\left(1+2+3+4\right)+...+\frac{1}{20}\left(1+2+3+...+20\right)\)
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Những câu hỏi liên quan
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
\(B=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{20}\left(1+2+3+...+20\right)\)
\(=1+\frac{1}{2}\cdot\frac{2\cdot3}{2}+\frac{1}{3}\cdot\frac{3\cdot4}{2}+...+\frac{1}{20}\cdot\frac{20\cdot21}{2}\)
\(=\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+\frac{5}{2}+...+\frac{21}{2}\)
\(=\frac{1+2+3+....+21}{2}-\frac{1}{2}\)
\(=\frac{21\cdot22}{2}\cdot\frac{1}{2}-\frac{1}{2}\)
\(=\frac{1}{2}\left(\frac{21\cdot22}{2}-1\right)\)
\(=230\cdot\frac{1}{2}\)
Bí
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
\(\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+....+\frac{1}{\sqrt{100}}>10\)
HH
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!)
\(B=\left(1+2+3+....+10\right)+\left(1+2+3+...+10\right)+\left(\frac{1}{2}.10\right)\)
\(B=55+55+5=115\)
BT
16 tháng 5 2017
Ta có: 1+2+3+...+n=\(\frac{n\left(n+1\right)}{2}\)
=> \(1=\frac{1x2}{2};\frac{1}{2}\left(1+2\right)=\frac{2x3}{2x2};\frac{1}{3}\left(1+2+3\right)=\frac{3x4}{2x3};\)\(;\frac{1}{4}\left(1+2+3+4\right)=\frac{4x5}{2x4};...;\frac{1}{20}\left(1+2+3+...+20\right)=\frac{20x21}{2x20}\)
=> \(B=\frac{1x2}{2}+\frac{2x3}{2x2}+\frac{3x4}{2x3}+\frac{4x5}{2x4}+...+\frac{20x21}{2x20}\)
=> \(B=\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+\frac{5}{2}+...+\frac{21}{2}\)
=> \(B=\frac{1}{2}\left(2+3+4+5+...+21\right)=\frac{1}{2}\left(\frac{21.22}{2}-1\right)\)
=> \(B=\frac{230}{2}=115\)
Đáp số: B=115
\(B=1+\frac{1}{2}.\frac{2.3}{2}+\frac{1}{3}.\frac{3.4}{2}+\frac{1}{4}.\frac{4.5}{2}+.....+\frac{1}{20}.\frac{20.21}{2}\)
\(B=\frac{2}{2}+\frac{2.3:2}{2}+\frac{3.4:3}{2}+.....+\frac{20.21:20}{2}\)
\(B=\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+\frac{5}{2}+....+\frac{21}{2}\)
\(B=\frac{2+3+.....+21}{2}\)
\(B=\frac{\left(2+21\right).20}{2}:2=\frac{230}{2}:2=165:2=\frac{165}{2}\)