Question

tính tổng :

a= 4/5.8 + 4/8.11 + 4/11.14 + ... + 4/305.308

các bạn nhơ giải chi tiết nha.

mình xin cảm ơn.

Answer 1

Ta có: \(A=\frac{4}{5.8}+\frac{4}{8.11}+\frac{4}{11.14}+...+\frac{4}{305.308}\)

\(\frac{3}{4}A=\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{305.308}\)

\(\frac{3}{4}A=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{305}-\frac{1}{308}\)

\(\frac{3}{4}A=\frac{1}{5}-\frac{1}{308}\)

\(\frac{3}{4}A=\frac{303}{1540}\)

\(\Rightarrow A=\frac{303}{1450}\div\frac{3}{4}\)

\(\Rightarrow A=\frac{101}{385}\)

Nhớ k mình nha.

Answer 2

\(A=\frac{4}{5.8}+\frac{4}{8.11}+\frac{4}{11.14}+...+\frac{4}{305.308}\)

\(\frac{3}{4}A=\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{305.308}\)

\(\frac{3}{4}A=\frac{1}{5}-\frac{1}{8}+\frac{1}{8} -\frac{1}{11}+...+\frac{1}{305}-\frac{1}{308}\)

\(\frac{3}{4}A=\frac{1}{5}-\frac{1}{308}=\frac{303}{1540}\)

\(A=\frac{308}{1540}:\frac{3}{4}=\frac{4}{15}\)