Question

tính hợp lí:

3/3.5 + 3/5.7 + 3/7.9 + ...... + 3/47.49

Answer 1

Đặt A = \(\dfrac{3}{3.5}+\dfrac{3}{5.7}+\dfrac{3}{7.9}+...+\dfrac{3}{47.49}\)

2A = \(\dfrac{3.2}{3.5}+\dfrac{3.2}{5.7}+\dfrac{3.2}{7.9}+...+\dfrac{3.2}{47.49}\)

2A = 3\(\left(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+...+\dfrac{2}{47.49}\right)\)

2A = 3 \(\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{47}-\dfrac{1}{49}\right)\)

2A = 3 \(\left(\dfrac{1}{3}-\dfrac{1}{49}\right)\)

2A = 3 . \(\dfrac{46}{147}\)

2A = \(\dfrac{46}{49}\)

=> A = \(\dfrac{46}{49}\) : 2

=> A = \(\dfrac{23}{49}\)