Question

[Hiếu Trung]

Tính tổng:

1/2×3+1/3×4+.....+1/49×50

Giúp mình với

Answer 1

[Nguyễn Hoàng Phúc]

\(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)

=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)

=\(\frac{1}{2}-\frac{1}{50}\)

=\(\frac{12}{25}\)

Dấu chấm là dấu nhân,bạn bít rồi đúng ko

Answer 2

[Five centimeters per second]

\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{49\cdot50}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)

\(=\frac{1}{2}-\frac{1}{50}=\frac{25}{50}-\frac{1}{50}=\frac{24}{50}=\frac{12}{25}\)

Công thức : \(\frac{a}{b\left(b+a\right)}=\frac{1}{b}-\frac{1}{b+a}\)

\(\frac{2a}{b\left(b+a\right)\left(b+2a\right)}=\frac{1}{b\left(b+a\right)}-\frac{1}{\left(b+a\right)\left(b+2a\right)}\)

\(\frac{3a}{b\left(b+a\right)\left(b+2a\right)\left(b+3a\right)}=\frac{1}{b\left(b+a\right)\left(b+2a\right)}-\frac{1}{\left(b+a\right)\left(b+2a\right)\left(b+3a\right)}\)