Question

[le thi huong giang]

Tinh tong

S4=3/50+3/150+3/300+...+3/9500

S5=55/11*16+55/16*21+55/21*26+...+55/36*41

Answer 1

[Đặng Quỳnh Ngân]

a) \(S4=\frac{3}{50}+\frac{3}{150}+\frac{3}{300}+...+\frac{3}{9500}\)

\(S4=\frac{3}{5.10}+\frac{3}{10.15}+\frac{3}{15.20}+...+\frac{3}{95.100}\)

\(S4=\frac{3}{5}\left(\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+\frac{1}{15}-\frac{1}{20}+...+\frac{1}{95}-\frac{1}{100}\right)\)

\(S4=\frac{3}{5}\left(\frac{1}{5}-\frac{1}{100}\right)\)

\(S4=\frac{3}{5}.\frac{19}{100}\)

\(S4=\frac{57}{500}\Rightarrow S=\frac{57}{500}:4=\frac{57}{2000}\)

b) \(S5=\frac{55}{11.16}+\frac{55}{16.21}+...+\frac{55}{36.41}\)

\(S5=\frac{55}{5}.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{36}-\frac{1}{41}\right)\)

\(S5=11.\left(\frac{1}{11}-\frac{1}{41}\right)\)

\(S5=11.\frac{30}{451}\)

\(S5=\frac{30}{41}\Rightarrow S=\frac{30}{41}:5=\frac{6}{41}\)

Answer 2

[Đặng Quỳnh Ngân]

Mình không hiểu ý bạn là S.4 hay là S4 là tên