Question

Tính tổng sau:

\(S=\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+....+\frac{1}{17.20}\)

giải giúp mình nka

Answer 1

S = 1/3 . (1/2 - 1/5 + 1/5 - 1/8 + ... + 1/17 - 1/20)

   = 1/3 . (1/2 - 1/20)

   = 1/3 . 9/20

   = 3/20

Answer 2

\(3S=\frac{5-2}{2.5}+\frac{8-5}{5.8}+\frac{11-8}{8.11}+...+\frac{20-17}{17.20}\)

\(3S=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{17}-\frac{1}{20}=\frac{1}{2}-\frac{1}{20}=\frac{9}{20}\)

\(S=\frac{9}{20}:3=\frac{3}{20}\)

Answer 3

\(S=\frac{1}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+...........+\frac{3}{17.20}\right)\)

\(=\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+.........+\frac{1}{17}-\frac{1}{20}\right)\)

\(=\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{20}\right)\)

\(=\frac{1}{3}.\left(\frac{10}{20}-\frac{1}{20}\right)\)

\(=\frac{1}{3}.\frac{9}{20}\)

\(-\frac{3}{20}\)

Answer 4

S = 1/2 .5 + 1/5.8+1/8.11+.......+1/17.20

S = 3.{   1/2 .5 + 1/5.8+1/8.11+.......+1/17.20}

= 3/2.5+3/5.8+3/8.11+.....+3/20

S = 1/2 + (-1/ 5 + 1/5) + -1/8 +18 +.......+ -1/17+1/20

S =  1/2 +1/20 = 10/20 + 1/20 = 21/20 .

Answer 5

S=1/2x5 + 1/5x8 +1/8x11+...+1/17x20

S=1/3 x (1/2 - 1/5) + 1/3 x (1/5 - 1/8) +1/3 x( 1/8 - 1/11) +...+ 1/3 x (1/17 - 1/20)

S=1/3x(1/2 -1/5 + 1/5 -1/8 + 1/8 -1/11 +...+1/17 - 1/20)

(bỏ tất cả các phân số trong ngoặc chỉ để lại p/s đầu và p/s cuối)

S=1/3 x (1/2 - 1/20)

S=1/3 x 9/20

S=3/20