Tính: 4/1×3+16/3×5+36/5×7+…….+2500/49×51

04/08/2021 Bởi Nevaeh

Tính:
4/1×3+16/3×5+36/5×7+…….+2500/49×51

0 bình luận về “Tính: 4/1×3+16/3×5+36/5×7+…….+2500/49×51”

anhthu

04/08/2021 vào lúc 16:24

$S = \frac{4}{1 \times 3} + \frac{16}{3 \times 5} + \frac{36}{5 \times 7} + . . . + \frac{2500}{49 \times 51}$

$= \frac{1 \times 3 + 1}{1 \times 3} + \frac{3 \times 5 + 1}{3 \times 5} + \frac{5 \times 7 + 1}{5 \times 7} + . . . + \frac{49 \times 51 + 1}{49 \times 51}$

$= \frac{1 \times 3}{1 \times 3} + \frac{1}{1 \times 3} + \frac{3 \times 5}{3 \times 5} + \frac{1}{3 \times 5} + \frac{5 \times 7}{5 \times 7} + \frac{1}{5 \times 7} + . . . + \frac{49 \times 51}{49 \times 51} + \frac{1}{49 \times 51}$

$= 1 + \frac{1}{1 \times 3} + 1 + \frac{1}{3 \times 5} + 1 + \frac{1}{5 \times 7} + . . . + \frac{1}{49 \times 51}$

$= 25 + \frac{1}{1 \times 3} + \frac{1}{3 \times 5} + \frac{1}{3 \times 5} + \frac{1}{5 \times 7} + . . . + \frac{1}{49 \times 51}$

$= 25 + \frac{1}{2} \times (1 - \frac{1}{3}) + \frac{1}{2} \times (\frac{1}{3} - \frac{1}{5}) + \frac{1}{2} \times (\frac{1}{5} - \frac{1}{7}) + . . . + \frac{1}{2} \times (\frac{1}{49} - \frac{1}{51})$

$= 25 + \frac{1}{2} \times (1 - \frac{1}{3} + \frac{1}{3} - \frac{1}{5} + \frac{1}{5} - \frac{1}{7} + . . . + \frac{1}{49} - \frac{1}{51})$

$= 25 + \frac{1}{2} \times (1 - \frac{1}{51})$

$= 25 + \frac{1}{2} \times \frac{50}{51}$

$= 25 + \frac{25}{51}$

$= \frac{1300}{51}$
Bình luận

Viết một bình luận Hủy