a.
\(1+2+3+...+n=820\)
\(\Leftrightarrow\dfrac{n\left(n+1\right)}{2}=820\)
\(\Leftrightarrow n\left(n+1\right)=1640\)
\(\Leftrightarrow n\left(n+1\right)=40.41\)
\(\Rightarrow n=40\)
b.
\(\left(n+5\right)⋮\left(n+1\right)\)
\(\Rightarrow\left(n+1\right)+1⋮n+1\)
\(\Rightarrow n+1=Ư\left(1\right)\)
\(\Rightarrow\left[{}\begin{matrix}n+1=-1\\n+1=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}n=-2\notin N\left(loại\right)\\n=0\end{matrix}\right.\)
c.
\(\left(2n+7\right)⋮\left(n+2\right)\)
\(\Rightarrow\left(2n+4+3\right)⋮\left(n+2\right)\)
\(\Rightarrow2\left(n+2\right)+3⋮\left(n+2\right)\)
\(\Rightarrow3⋮\left(n+2\right)\)
\(\Rightarrow n+2=Ư\left(3\right)=\left\{-3;-1;1;3\right\}\)
Do n tự nhiên \(\Rightarrow n\ge0\Rightarrow n+2\ge2\)
\(\Rightarrow n+2=3\)
\(\Rightarrow n=1\)
