Question

Bài 1:Tính tổng

S=\(\frac{14}{3.5}+\frac{14}{5.7}+\frac{14}{7.9}+...+\frac{14}{61.63}\) so sánh với \(\frac{5}{2}\)

Help meeeeeeeeeeeeeeeee

Lớp 6

 

Answer 1

\(S=7(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{61}-\frac{1}{63}) \)

\(S=7(\frac{1}{3}-\frac{1}{63})\)

\(S=7(\frac{21}{63}-\frac{1}{63}) \)

\(S=7.\frac{20}{63}\)

\(S=\frac{20}{9}\)

Do đó:\(S<\frac{5}{2}\)

Answer 2

S=\(\frac{2.7}{3.5}+\frac{2.7}{5.7}+\frac{2.7}{7.9}+....+\frac{2.7}{61.63}\)và\(\frac{5}{2}\)

S=7.(\(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+.....-\frac{1}{63}\)) và\(\frac{5}{2}\)

S=7.(\(\frac{1}{3}-\frac{1}{63}\)) và\(\frac{5}{2}\)

S=7.\(\frac{20}{63}\)và\(\frac{5}{2}\)

=>S=\(\frac{20}{9}\)so với \(\frac{5}{2}\)

=>S=\(\frac{40}{18}\)và\(\frac{45}{18}\)

=>S<\(\frac{5}{2}\)