rozwiąż równanie :
-5+8+21+....+x=1899
a₁=-5
S=1899
r=13
an=x
Sn=(a₁+an)n/2
an=a₁+(n-1)r
an=-5+(n-1)*13
an=-5+13n-13
an=13n-18
1899=(-5+13n-18)n/2
3798=(13n-23)n
3798=13n²-23n
13n²-23n-3798=0
Δ=(-23)²-4*13*(-3798)
Δ=529+197496
Δ=198025
√Δ=445
n₁=(-(-23)-445)/(2*13)
n₁=-422/26
n₁=-211/13 ⇐ odpada bo n∉N
n₂=(-(-23)+445)/(2*13)
n₂=-468/26
n₂=18
an=13*18-18
an=234-18
an=216 ⇒ x=216
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a₁=-5
S=1899
r=13
an=x
Sn=(a₁+an)n/2
an=a₁+(n-1)r
an=-5+(n-1)*13
an=-5+13n-13
an=13n-18
1899=(-5+13n-18)n/2
3798=(13n-23)n
3798=13n²-23n
13n²-23n-3798=0
Δ=(-23)²-4*13*(-3798)
Δ=529+197496
Δ=198025
√Δ=445
n₁=(-(-23)-445)/(2*13)
n₁=-422/26
n₁=-211/13 ⇐ odpada bo n∉N
n₂=(-(-23)+445)/(2*13)
n₂=-468/26
n₂=18
an=13*18-18
an=234-18
an=216 ⇒ x=216