Question

Tìm n biết :1+2+3+4+5+.....+n=210

 

Answer 1

1 + 2 + 3 + 4 + 5 + ..... + n = 210

=> 2 . ( 1 + 2 + 3 + 4 + 5 + ........ + n ) = 210

=>  1 + 2 + 3 + 4 + 5 + ....... + n  = 210 : 2

=> 1 + 2 + 3 + 4 + 5 + ..... + n = 105

=> n . ( n + 1 ) : 2 =  105

n . ( n + 1 ) = 105 x 2

n . ( n + 1 ) = 210

Vì 14 . 15 = 210

=> n = 14

Answer 2

\(1+2+3+4+5+..+n=210\)

\(\Rightarrow2.\left(1+2+3+4+5+...+n\right)=210\)

\(\Rightarrow1+2+3+4+5+...+n=210:2\)

\(\Rightarrow1+2+3+4+5+...+n=105\)

\(\Rightarrow n.\left(n+1\right):2=105\)

\(\Rightarrow n.\left(n+1\right)=210\)

Vì \(14.15=210\)

\(\Rightarrow n=14\)