Question

[nguyen mai phuong]

tinh nhanh

A= 11+14+17+...+62+65

B=1/3 +1/15+1/35+1/63+1/99

C=3/10+3/40+3/88+3/154

D=3/5*7 + 3/7*9 +...+ 3/41*43 + 3/43*45

E=2003*2004/2003*2004+1 và 2004/2003

G=9*(151515/171717 + 131313/181818)

con nào làm đc thì làm trước nha. đang vội

Answer 1

[Đức Phạm]

\(A=11+14+17+...+62+65\)

Số số hạng của \(A\)là 

\(\left(65-11\right)\div3+1=19\)(số hạng)

Tổng của \(A\)là: 

\(\left(11+65\right)\times19\div2=722\)

Đáp số: 722

\(B=\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}\)

\(B=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\)

\(B=\left(\frac{3-1}{1.3}+\frac{5-3}{3.5}+.....+\frac{9-7}{7.9}+\frac{11-9}{9.11}\right)\times\frac{1}{2}\)

\(B=\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+.....+\frac{1}{9}-\frac{1}{11}\right)\times\frac{1}{2}\)

\(B=\left(1-\frac{1}{11}\right)\times\frac{1}{2}\)

\(B=\frac{10}{11}\times\frac{1}{2}\)

\(B=\frac{5}{11}\)

\(C=\frac{3}{10}+\frac{3}{40}+\frac{3}{88}+\frac{3}{154}\)

\(C=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}\)

\(C=\left(\frac{3}{2}-\frac{3}{5}+\frac{3}{5}-\frac{3}{8}+....+\frac{3}{11}-\frac{3}{14}\right)\div3\)

\(C=\left(\frac{3}{2}-\frac{3}{14}\right)\div3\)

\(C=\frac{9}{7}\div3\)

\(C=\frac{3}{7}\)

Answer 2

[Nguyễn Tiến Dũng]

\(B=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\)

\(B=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)

\(B=1-\frac{1}{11}\)

\(B=\frac{10}{11}\)