Ta có:
\(S=\dfrac{2.8}{1.9}.\dfrac{3.9}{2.10}.\dfrac{4.10}{3.11}...\dfrac{42.48}{41.49}\)
\(S=\dfrac{2.3.4...42}{1.2.3...41}.\dfrac{8.9.10...48}{9.10.11...49}\)
\(S=\dfrac{42}{1}.\dfrac{8}{49}\)
\(S=\dfrac{48}{7}\)
Giải:
\(S=\dfrac{16}{9}.\dfrac{27}{20}.\dfrac{40}{33}.\dfrac{55}{48}.....\dfrac{2016}{2009}.\)
\(=\dfrac{2.8}{1.9}.\dfrac{3.9}{2.10}.\dfrac{4.10}{3.11}.\dfrac{5.11}{4.12}.....\dfrac{42.48}{41.49}.\)
\(=\dfrac{\left(2.3.4.5.....42\right)\left(8.9.10.11.....48\right)}{\left(1.2.3.4.....41\right)\left(9.10.11.12.....49\right)}.\)
\(=\dfrac{2.3.4.5.....42}{1.2.3.4.....41}.\dfrac{8.9.10.11.....48}{9.10.11.12.....49}.\)
\(=42.\dfrac{8}{49}.\)
\(=\dfrac{42.8}{49}.\)
\(=\dfrac{6.8}{7}.\)
\(=\dfrac{48}{7}.\)
Vậy \(S=\dfrac{48}{7}.\)
CHÚC BN HỌC TỐT!!! ^ - ^
Đừng quên bình luận nếu bài mik sai nhé!!!
Còn nếu bài mik đúng thì nhớ tick cho mik để mik lấy SP nha!!!
