Ta có : B = \(\frac{4}{1.4}+\frac{4}{4.7}+\frac{4}{7.10}+......+\frac{4}{2014.2017}\)
\(=\frac{4}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+......+\frac{3}{2014.2017}\right)\)
\(=\frac{4}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+......+\frac{1}{2014}-\frac{1}{2017}\right)\)
\(=\frac{4}{3}.\left(1-\frac{1}{2017}\right)\)
\(=\frac{4}{3}.\frac{2016}{2017}=\frac{2688}{2017}\)
3/4B = 3/4. (4/1.4+4/4.7+4/7.10+...+4/2014.2017)
3/4B = 3/1.4 +3/4.7 +3/7.10 +....+ 3/2014.2107
3/4B = 1-1/4+1/4-1/7+1/7-1/10+...+1/2014-1/2017
3/4B =1-1/2017
3/4B =2016/2017
B = 2016/2017 :3/4
B = 2688/2017
B=4/1.4 +4/4.7 +4/7.10 +...+4/2014.2017
B=4/1-4/4+4/4-4/7+4/7-4/10+...+4/2014-4/2017
B=4-4/2017
B=8064/2017
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