Question

tính nhanh: 

C=\(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+........+\frac{1}{2499}\)

Answer 1

\(C=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+.....+\frac{1}{49.51}\)

\(C=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{49}-\frac{1}{51}\right)\)

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

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

Answer 2

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

\(C=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{51}\right)=\frac{8}{51}\)

Answer 3

C=\(\frac{1}{3.5}\)+\(\frac{1}{5.7}\)+\(\frac{1}{7.9}\)+......+\(\frac{1}{49.51}\)

C=(\(\frac{2}{3.5}\)+\(\frac{2}{5.7}\)+\(\frac{2}{7.9}\)+.......+\(\frac{2}{49.51}\)) :2

C=(\(\frac{1}{3}\)-\(\frac{1}{5}\)+\(\frac{1}{5}\)-\(\frac{1}{7}\)+\(\frac{1}{7}\)-\(\frac{1}{9}\)+....+\(\frac{1}{49}\)-\(\frac{1}{51}\)) :2

C=(\(\frac{1}{3}\)-\(\frac{1}{51}\)) :2

C=\(\frac{16}{51}\):2=\(\frac{8}{51}\)