Question

el termino general (formula) de las siguientes sucesiones:
An: 2,6,24,120..
An: 1/5,-1/10,1/15,-1/20 ..​

Answer 1

caso 1:

2=1×2=2!=(1+1)!

6=1×2×3=3!=(2+1)!

24=1×2×3×4=4!=(3+1)!

120=1×2×3×4×5=5!=(4+1)!

en general

An=(n+1)!

caso 2:

1/5=(-1)^0/(5×1)=(-1)^(1-1)/(5×1)

-1/10=(-1)^1/(5×2)=(-1)^(2-1)/(5×2)

1/15=(-1)^2/(5×3)=(-1)^(3-1)/(5×3)

-1/20=(-1)^2/(5×4)=(-1)^(4-1)/(5×4)

en general

An=(-1)^(n-1)/(5n)