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2 tháng 8 2015

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

=\(\frac{2}{2}+\frac{3}{2}+\frac{6}{3}+...+\frac{136}{16}\)

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

=\(\frac{2+3+4+5+6+...+17}{2}\)=\(\frac{152}{2}=76\)

9 tháng 11 2018

Ta có:

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

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

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

\(=\frac{\frac{23.20}{2}}{2}=\frac{23.10}{2}=115\)

16 tháng 7 2017

Ta có ; K = \(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+.....+\frac{1}{45}\)

\(=1+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+....+\frac{2}{90}\)

\(=1+\left(\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+.....+\frac{2}{9.10}\right)\)

\(=1+2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+.....+\frac{1}{9.10}\right)\)

\(=1+2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{9}-\frac{1}{10}\right)\)

\(=1+2\left(\frac{1}{2}-\frac{1}{10}\right)\)

\(=1+1-\frac{1}{5}\)(nhân phá ngoặc)

\(=2-\frac{1}{5}\)< 2 

Vậy K = \(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+.....+\frac{1}{45}\)< 2

8 tháng 1 2016

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

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

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

\(=\frac{\left(2+21\right).20:2}{2}=\frac{230}{2}=115\)

8 tháng 1 2016

Số cuối là

\(\frac{1}{10}.\left(1+2+3+...+10\right)\) hay \(\frac{1}{20}.\left(1+2+3+...+20\right)\) ??

31 tháng 3 2018

=1+1/2.(3.2/2)+1/3.(4.3/2)+1/4.(5.4/2)+...+1/20.(21.20/2)

=1+3/2+2+5/2+...+21/2 ( rút gọn)

=2/2+3/2+4/2+5/2+...+21/2

=(2+3+4+5+...+21)/2=(20.23)/2.2=(20.23)/4

=23.5=115

Ko bt mk lm dung ko nx?