Question

Cho A = 1/10 + 1/15 + 1/21 +....+ 1/120 Tìm x sao cho A :x = 759

Answer 1

\(A=\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+...+\dfrac{1}{120}\)
\(=2\left(\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+...+\dfrac{1}{240}\right)\)
\(=2\left(\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+...+\dfrac{1}{15.16}\right)\)
\(=2\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+...+\dfrac{1}{15}-\dfrac{1}{16}\right)\)
\(=2\left(\dfrac{1}{4}-\dfrac{1}{16}\right)\)
\(=2\cdot\dfrac{3}{16}\)
\(=\dfrac{3}{8}\)
\(A:x=759\)
\(\dfrac{3}{8}:x=759\)
\(\Rightarrow x=\dfrac{3}{8}:759=\dfrac{1}{2024}\)
#AvoidMe

Answer 2

A=2(1/20+1/30+...+1/240)

=2(1/4-1/5+1/5-1/6+...+1/15-1/16)

=2*3/16=3/8

A:x=759

=>x=3/8:759=1/2024

Answer 3

1/2A=1/20+1/30*1/42+...+1/240
1/2A=1/4*5+1/5*6+1/6*7+...+1/15*16
1/2A=1/4-1/5+1/5-1/6+1/6-1/7+...1/15-1/16
1/2A=1/4-1/16=3/16
A=3/16:1/2 A=3/8
Ta có: A: x =759
        3/8: x =759
                x=3/8 : 759 = 1/2024