tương tự câu này bạn ơi bạn đọc và làm bài của mình nhé

 S=1+2+2²+....+2²⁰¹²

          A.2    =2+2²+2³+.........+2²⁰¹³

          A.2-A=2²⁰¹³-1

            A=2²⁰¹³-1

Ta thấy: 2²⁰¹³-1 < 2²⁰¹³

qua de dang nhe

S=1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+...+1/(1+2+3+4+...+10)

S=1/(2*3/2)+1/(3*4/2)+1/(4*5/2)+...+1/(10*11/2)

S=2(1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+...+1/(10*11)

S=2(1/2-1/3+1/3-1/4+1/4-1/5+...+1/10-1/11)

S=2(1/2-1/11)

S=2*9/22

S=9/11

nho k cho minh voi nha

\(S=\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+...+10}\)

\(S=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{55}\)

\(S=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{110}\)

\(S=2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{110}\right)\)

\(S=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{10.11}\right)\)

\(S=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\right)\)

\(S=2\left(\frac{1}{2}-\frac{1}{11}\right)\)

\(S=2.\frac{9}{22}\)

\(S=\frac{9}{11}\)

1.

a) \(\frac{6}{15}+\frac{6}{35}+\frac{6}{63}+\frac{6}{99}+\frac{6}{143}\)

\(=\frac{6}{3.5}+\frac{6}{5.7}+\frac{6}{7.9}+\frac{6}{9.11}+\frac{6}{11.13}\)

\(=\frac{6}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{11}-\frac{1}{13}\right)\)

\(=\frac{6}{2}\left(\frac{1}{3}-\frac{1}{13}\right)\)

\(=\frac{6}{2}.\frac{10}{39}\)

\(=\frac{10}{13}\)

b) \(\frac{3}{24}+\frac{3}{48}+\frac{3}{80}+\frac{3}{120}+\frac{3}{168}\)

\(=\frac{3}{4.6}+\frac{3}{6.8}+\frac{3}{8.10}+\frac{3}{10.12}+\frac{3}{12.14}\)

\(=\frac{3}{2}\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+...+\frac{1}{12}-\frac{1}{14}\right)\)

\(=\frac{3}{2}.\left(\frac{1}{4}-\frac{1}{14}\right)\)

\(=\frac{3}{2}.\frac{5}{28}\)

\(=\frac{15}{56}\)

\(a.\frac{6}{3.5}+\frac{6}{5.7}+...+\frac{6}{11.13}\)

\(=3.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\right)\)

\(=3.\left(\frac{1}{3}-\frac{1}{13}\right)\)

\(=3.\frac{10}{39}\)

\(=\frac{10}{13}\)

\(a.\frac{6}{15}+\frac{6}{35}+\frac{6}{63}+\frac{6}{99}+\frac{6}{143}\)

\(=\frac{6}{3.5}+\frac{6}{5.7}+\frac{6}{7.9}+\frac{6}{9.11}+\frac{6}{11.13}\)

\(=3.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)

\(=3.\left(\frac{1}{3}-\frac{1}{13}\right)\)

\(=3.\frac{10}{39}\)

\(=\frac{10}{13}\)

\(\frac{4}{3}-\left(x-\frac{1}{5}\right)=\left|\frac{-3}{10}+\frac{1}{2}\right|-\frac{1}{6}\)

\(\frac{4}{3}-\left(x-\frac{1}{5}\right)=\frac{1}{5}-\frac{1}{6}\)

\(\frac{4}{3}-\left(x-\frac{1}{5}\right)=\frac{1}{30}\)

\(x-\frac{1}{5}=\frac{4}{3}-\frac{1}{30}\)

\(x-\frac{1}{5}=\frac{13}{10}\)

\(x=\frac{13}{10}+\frac{1}{5}\)

\(x=\frac{3}{2}\)