1/2+1/2^2+1/2^3+.....+1/2^20
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BM
1
30 tháng 1 2024
\(1+\dfrac{1}{2}\left(1+2\right)+\dfrac{1}{3}\left(1+2+3\right)+...+\dfrac{1}{20}\left(1+2+3+...+20\right)\)
\(=1+\dfrac{1}{2}\cdot\dfrac{2\cdot3}{2}+\dfrac{1}{3}\cdot\dfrac{3\cdot4}{2}+...+\dfrac{1}{20}\cdot\dfrac{20\cdot21}{2}\)
\(=1+\dfrac{3}{2}+\dfrac{4}{2}+...+\dfrac{21}{2}\)
\(=\dfrac{2+3+4+...+21}{2}=\dfrac{\left(21+2\right)+\left(3+20\right)+...+\left(10+13\right)+\left(11+12\right)}{2}\)
\(=\dfrac{23+23+...+23}{2}=\dfrac{23\cdot10}{2}=23\cdot5=115\)
TK
0
TT
1
IM
0
H
0
TQ
3
2 tháng 3 2017
\(B=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{20}\left(1+2+3+...+20\right)\)
\(=1+\frac{1}{2}.\frac{2\left(2+1\right)}{2}+\frac{1}{3}.\frac{3\left(3+1\right)}{2}+...+\frac{1}{20}.\frac{20\left(20+1\right)}{2}\)
\(=\frac{2}{2}+\frac{2+1}{2}+\frac{3+1}{2}+...+\frac{20+1}{2}\)
\(=\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+...+\frac{20}{2}\)
\(=\frac{2+3+4+...+20}{2}=\frac{\frac{20\left(20+1\right)}{2}-1}{2}=\frac{209}{2}\)
KT
0
2 tháng 1 2016
\(B=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{20}\left(1+2+3+...+20\right)\)
\(=1+\frac{1}{2}.2.3:2+\frac{1}{3}.3.4:2+...+\frac{1}{20}.20.21:2\)
=\(\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+...+\frac{21}{2}=\frac{2+3+4+...+21}{2}=\frac{230}{2}=115\)
bằng 1-1/2^19 nhé
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