Question

[lqhiuu]

tính tổng;

C= 1/15+1/35+...+1/2499

GIÚP MK NHA

Answer 1

[Nguyễn Huy Tú]

\(C=\dfrac{1}{15}+\dfrac{1}{35}+...+\dfrac{1}{2499}\)

\(=\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{49.51}\)

\(=\dfrac{1}{2}\left(\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{49.51}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{49}-\dfrac{1}{51}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{51}\right)\)

\(=\dfrac{1}{2}.\dfrac{16}{51}=\dfrac{8}{51}\)

Vậy \(C=\dfrac{8}{51}\)

Answer 2

[Quốc Đạt]

\(\Rightarrow C=\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{49.51}\)

\(C=\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{49}-\dfrac{1}{51}\right)\)

\(C=\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{51}\right)\)

\(C=\dfrac{1}{2}.\dfrac{15}{51}\)

\(C=\dfrac{8}{51}\)