Lim ((n+2) ! + (n+1) !) / (n+3) !

n-бескон.

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Математика

Маркел

6 марта, 09:03

Lim ((n+2) ! + (n+1) !) / (n+3) !

n-бескон.

+5

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Ванда · Answer 1

Lim ((n+2) ! + (n+1) !) / (n+3) ! = lim ((n+1) ! * (n+2) + (n+1) !) / ((n+1) ! * (n+2) * (n+3)) =

lim ((n+1) ! (n+2+1)) / ((n+1) ! * (n+2) * (n+3)) = lim (n+3) / ((n+2) * (n+3)) =

lim (n+3) / (n²+5n+6) = lim (1/n+3/n²) / (1+5/n+6/n²) = 0/1=0

Lim ((n+2) ! + (n+1) !) / (n+3) !n-бескон.

Lim ((n+2) ! + (n+1) !) / (n+3) !

n-бескон.