a) \(\frac{53}{101}\cdot-\frac{13}{97}+\frac{53}{101}\cdot-\frac{84}{97}\)

\(=\frac{53}{101}\cdot\left(-\frac{13}{97}-\frac{84}{97}\right)\)

\(=\frac{53}{101}\cdot\left(-1\right)\)

\(=-\frac{53}{101}\)

giống huy nhé

\(A=\left(\dfrac{1}{4}-1\right)\left(\dfrac{1}{9}-1\right)\left(\dfrac{1}{16}-1\right)...\left(\dfrac{1}{100}-1\right)\)

\(A=-\dfrac{3}{4}.\left(-\dfrac{8}{9}\right).\left(-\dfrac{15}{16}\right)...\left(-\dfrac{99}{100}\right)\)

\(A=\dfrac{\left(-1\right).3}{2^2}.\dfrac{\left(-2\right).4}{3^2}.\dfrac{\left(-3\right).5}{4^2}....\dfrac{\left(-9\right).11}{10^2}\)

\(A=\dfrac{\left(-1\right).\left(-2\right).\left(-3\right)....\left(-9\right)}{2.3.4....10}.\dfrac{3.4.5....11}{2.3.4....10}\)

\(A=\dfrac{-1}{10}.\dfrac{11}{2}=-\dfrac{11}{20}\)

Câu B tương tự nha bạn!!!

\(A=\left(\dfrac{1}{4}-1\right)\left(\dfrac{1}{9}-1\right)\left(\dfrac{1}{16}-1\right)...\left(\dfrac{1}{100}-1\right)\)

\(A=\dfrac{-3}{4}.\dfrac{-8}{9}.\dfrac{-15}{16}......\dfrac{-99}{100}\)

\(A=\dfrac{-1.3}{2.2}.\dfrac{-2.4}{3.3}.\dfrac{-3.5}{4.4}.....\dfrac{-9.11}{10.10}\)

\(A=\dfrac{-1.3.-2.4.-3.5.....-9.11}{2.2.3.3.4.4.....10.10}\)

\(A=\dfrac{-1.-2.-3......-9}{2.3.4......10}.\dfrac{3.4.5....11}{2.3.4...10}\)

\(A=\dfrac{-1}{10}.\dfrac{11}{2}=\dfrac{-11}{20}\)

\(B=\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right)\left(\dfrac{1}{4}-1\right).....\left(\dfrac{1}{10}-1\right)\)

\(B=\dfrac{-1}{2}.\dfrac{-2}{3}.\dfrac{-3}{4}........\dfrac{-9}{10}\)

\(B=\dfrac{-1.-2.-3......-9}{2.3.4......10}\)

\(B=\dfrac{-1}{10}\)

Câu 17:

\(\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).\left(1+\frac{1}{4}\right)...\left(1+\frac{1}{2006}\right).\left(1+\frac{1}{2007}\right)\)

=\(\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{2007}{2006}.\frac{2008}{2007}\)

\(=\frac{2008}{2}=1004\)

Câu 18:

\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{2006}\right).\left(1-\frac{1}{2007}\right)\)

\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{2005}{2006}.\frac{2006}{2007}\)

\(=\frac{1}{2007}\)

ban tra loi di

1+1-1+1=

giúp mik giải nhé. Cảm ơn các bạn nhiều

chỉ cần ns 1 từ dễ

😀

giúp mình với

Ta có:

  \(K=\frac{1}{7}+\frac{1}{91}+\frac{1}{247}+\frac{1}{475}+\frac{1}{775}+\frac{1}{1147}\)

     \(=\frac{1}{1.7}+\frac{1}{7.13}+\frac{1}{13.19}+\frac{1}{19.25}+\frac{1}{25.31}+\frac{1}{31.37}\)

     \(=\frac{1}{6}\left(1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+\frac{1}{13}-\frac{1}{19}+\frac{1}{19}-\frac{1}{25}+\frac{1}{25}-\frac{1}{31}+\frac{1}{31}-\frac{1}{37}\right)\)

      \(=\frac{1}{6}.\left(1-\frac{1}{37}\right)=\frac{1}{6}.\frac{36}{37}=\frac{6}{37}\)

K = \(\frac{1}{7}+\frac{1}{91}+\frac{1}{247}+\frac{1}{475}+\frac{1}{755}+\frac{1}{1147}=0,1621963429\)