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1-lim-n-3-n-2-n-6-n-and-lim-n-1-2-2-32-4-2-n-2-n-3-help-me-




Question Number 131202 by abdurehime last updated on 02/Feb/21
1        lim_(n→∞) (((3^n +2^n )/6^n )) and      ^( lim  _(n→∞) (((1+2^2 +32+4^2 +.......+n^2 )/n^3 )))   help me
1limn(3n+2n6n)andlimn(1+22+32+42+.+n2n3)helpme
Commented by liberty last updated on 02/Feb/21
 lim_(n→∞) (((1^2 +2^2 +3^2 +4^2 +...+n^2 )/n^3 ))
limn(12+22+32+42++n2n3)
Answered by liberty last updated on 02/Feb/21
 lim_(n→∞)  ((6^n (((3/6))^n +((2/6))^n ))/6^n ) = lim_(n→∞) [((1/2))^n +((1/3))^n ]   = 0 + 0 = 0
limn6n((36)n+(26)n)6n=limn[(12)n+(13)n]=0+0=0
Commented by EDWIN88 last updated on 03/Feb/21
it is right answer !
itisrightanswer!
Answered by Chhing last updated on 02/Feb/21
       =lim_(x→∞) ((((1/6)n(n+1)(2n+1))/n^3 ))       =(1/6)lim_(x→∞) (((n^3 (2+(3/n)+(1/n^2 )))/n^3 ))       =(1/6)×lim_(x→∞) (2+(3/n)+(1/n^2 ))       =(1/6)×2       =(1/3)
=limx(16n(n+1)(2n+1)n3)=16limx(n3(2+3n+1n2)n3)=16×limx(2+3n+1n2)=16×2=13
Answered by Ar Brandon last updated on 02/Feb/21
1.L=lim_(n→∞) (((3^n +2^n )/6^n ))=lim_(n→∞) {((3/6))^n +((2/6))^n }=0  2.T=lim_(n→∞) {((1+2^2 +3^2 +4^2 +∙∙∙+n^2 )/n^3 )}=lim_(n→∞) Σ_(k=1) ^n (k^2 /n^3 )          =lim_(n→∞) {(1/n)Σ_(k=1) ^n (k^2 /n^2 )}=∫_0 ^1 x^2 dx=(1/3)
1.L=limn(3n+2n6n)=limn{(36)n+(26)n}=02.T=limn{1+22+32+42++n2n3}=limnnk=1k2n3=limn{1nnk=1k2n2}=01x2dx=13