1+2+3+....+n = 820
<=> (1+n) . [ (n-1):1+1 ] :2 =820
<=> (n+1) . n :2 = 820
<=> (n+1).n = 820 . 2 = 1640
<=> n^2 + n = 1640
<=> n^2+n-1640 = 0
<=>(n^2-40n)+(41n-1640) = 0
<=> (n-40).(n+41) = 0
<=> n- 40 = 0 hoặc n+41 = 0
<=> n = 40 (t/m) hoặc n =-41(ko t/m)
Vậy n = 40
1+2+...+n = 820
=> \(\frac{n\left(n+1\right)}{2}=820\)
=> n(n + 1) = 1640
Mà 40.41 = 1640
=> n = 40
Vậy...
1 + 2 + 3 + 4 + ... + n = 820
n + ( n - 1 ) + ( n - 2 ) + ( n - 3 ) + ... + 1 = 820
( n + 1 ) + ( n + 1 ) + ( n + 1 ) + ...+ ( n + 1 ) = 820 + 820
=> n.( n + 1 ) = 820 . 2
<=> n2 + n + 1 = 1641
\(n^2+\frac{n}{2}+\frac{n}{2}+\frac{1}{4}+\frac{3}{4}=1641\)
\(\left(n+\frac{1}{2}\right)^2=1641-\frac{3}{4}=\frac{6561}{4}=\left(\frac{81}{2}\right)^2\)
\(\Rightarrow n+\frac{1}{2}=\frac{81}{2}\)
\(\Rightarrow n=40\)
\(1+2+3+4+...+n=820\)
\(\Rightarrow\frac{x\left(n+1\right)}{2}=820\)
\(\Rightarrow n\left(n+1\right)=1640\)
Mà \(40\times41=1640\)
\(\Rightarrow n=40\)
Vậy \(n=40\)
xét tổng vế trái=1+2+3+4+....+n
-tong tren co so cac so hang la:
(n-1):1+1=n(so hang)
-suy ra ve trai =(n+1).n:2
ma ve trai =820
suy ra (n+1).n:2=820
(n+1).n =820.2
(n+1).n =1640
ma n+1 va n la 2 so tu nhien lien tiep va 41.40=1640
suy ra n=40
