Question

求大神解答，求极限

求大神解答，求极限求大神解答

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Answer 1

(5)
lim(n->∞) (n^4 +n)^(1/5) /(n+2)
=lim(n->∞) (1 +1/n^3)^(1/5) /[n^(1/4)+ 2/n^(4/5) ]
=0
(6)
lim(n->∞) 5^n/[2.5^n +5(-2)^n ]
=lim(n->∞) 1/[2 +5(-2/5)^n ]
=1/2
(7)
1/(1x2)+1/(2x3)+...+1/[(n(n+1)]
=( 1- 1/2) +(1/2-1/3)+...+(1/n - 1/(n+1))
= 1- 1/(n+1)
lim(n->∞) [1/(1x2)+1/(2x3)+...+1/[(n(n+1)]]
=lim(n->∞) [1- 1/(n+1)]
=1
(8)
1/(1x3)+1/(3x5)+...+1/[(2n-1)(2n+1)]
=(1/2)[ ( 1-1/3)+(1/3-1/5) +...+(1/(2n-1) -1/(2n+1)) ]
=(1/2)( 1 -1/(2n+1))
lim(n->∞) [1/(1x3)+1/(3x5)+...+1/[(2n-1)(2n+1)]]
=lim(n->∞) (1/2)( 1 -1/(2n+1))
=1/2