Question

cho A = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 +.......+1/n

biết A = 39/40 tìm n

Answer 1

A = 1/2+1/6+1/12+1/20+1/30+...+1/n = 1/1.2  + 1/2.3 +1/3.4 + 1/4.5 + 1/5.6 ......+1/a.b ( a.b = n )

A = 1/2 + (1/2 -1/3) +( 1/3 -1/4) +(1/4 -1/5) +(1/5 -1/6) + ......

=> ( 1/a -1/b) = 1-1/b = 39/40 => b = 40 ; suy ra a = 39

Vậy n = 39 x 40 =1560

Answer 2

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{\left(n-1\right)n}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{n-1}-\frac{1}{n}\)

\(A=1-\frac{1}{n}\)

Mà A=\(\frac{39}{40}\Rightarrow\frac{39}{40}=1-\frac{1}{n}\)

Nên n=40