Question

2+4+6+...+n=110 tìm n 

Answer 1

2 + 4 + 6 + ... + n = 110

=> (n + 2) . n : 4 = 110

=> (n + 2) . n = 110 . 4

=> (n + 2) . n = 440

=> (n + 2) . n = 20 . 22

=> n + 2 = 22

=> n = 20

Answer 2

Áp dụng công thức tính dãy số ta có :

\(\frac{\left[\left(n-2\right):2+1\right].\left(n+2\right)}{2}=110\)

\(\left[\frac{n-2}{2}+1\right].\left(n+2\right)=220\)

\(\frac{n}{2}.\left(n+2\right)=220\)

\(\frac{n}{2}.n+\frac{n}{2}.2=220\)

\(\frac{n^2}{2}+n=220\)

\(\frac{n^2}{2}+\frac{2n}{2}=220\)

\(n^2+2n=440\)

\(n\left(n+2\right)=440\)

=> n = 20