Question

[Vũ Thị Ngọc Doan]

16/10 + 16/90 + 16/234 +...+ 16/3034 + 16/3690

Nhanh nha!

Answer 1

[Nguyễn Gia Khánh]

Ta đặt

\(A=\dfrac{16}{10}+\dfrac{16}{90}+...+\dfrac{16}{3034}+\dfrac{16}{3690}\)

\(A=\dfrac{8}{5}+\dfrac{8}{45}+...+\dfrac{8}{1517}+\dfrac{8}{1845}\)

\(A=\dfrac{8}{1\times5}+\dfrac{8}{5\times9}+...+\dfrac{8}{37\times41}+\dfrac{8}{41\times45}\)

\(\dfrac{4}{8}\times A=\dfrac{4}{1\times5}+\dfrac{4}{5\times9}+...+\dfrac{4}{37\times41}+\dfrac{4}{41\times45}\)

\(\dfrac{1}{2}\times A=1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{37}-\dfrac{1}{41}+\dfrac{1}{41}-\dfrac{1}{45}\)

\(\dfrac{1}{2}\times A=1-\dfrac{1}{45}\)

\(\dfrac{1}{2}\times A=\dfrac{44}{45}\)

\(A=\dfrac{44}{45}\times2\)

\(A=\dfrac{88}{45}\)