Question

tìm \(n\in\)N* biết :

a, 2+4+6+....+2n=210

b,1+2+3+...+n=210

c,n+(n+1)(n+2)+....+(n+30)=1240

Answer 1

c, \(n+\left(n+1\right)+\left(n+2\right)+...+\left(n+30\right)=1240\)

\(\rightarrow n+n+1+n+2+n+3+...+n+30=1240\)

\(\rightarrow\left(x+x+x+...+x\right)+\left(1+2+3+...+30\right)=1240\)

Từ 1 đến 30 có:

(30-1):1+1=30 (số)

\(\rightarrow31.x+\left(30+1\right).30:2=1240\)

\(31.x+31.15=1240\)

\(31.x+465=1240\)

\(31.x=1240-465\)

\(31.x=775\)

\(x=775:31\)

\(x=25\)

Answer 2

a) \(2+4+6+......+2n=210\)

\(\Leftrightarrow2\left(1+2+3+......+n\right)=210\)

\(\Leftrightarrow1+2+3+......+n=210:2\)

\(\Leftrightarrow1+2+3+......+n=105\)

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

\(\Leftrightarrow n\left(n+1\right)=105.2\)

\(\Leftrightarrow n\left(n+1\right)=210\)

Vì \(210=14.15\) \(\Rightarrow n=14\)

Answer 3

b, \(1+2+3+...+x=210\)

\(\rightarrow x.\left(x+1\right):2=210\)

\(x.\left(x+1\right)=420\)

\(x.\left(x+1\right)=20.21\)

\(\rightarrow x.\left(x+1\right)=20.\left(20+1\right)\)

\(\rightarrow x=20\)

Answer 4

b) \(1+2+3+.....+n=210\)

\(\Rightarrow n\left(n+1\right):2=210\)

\(\Rightarrow n\left(n+1\right)=210.2\)

\(\Rightarrow n\left(n+1\right)=420\)

Mà \(420=20.21\) \(\Rightarrow n=20\)