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lim(n->oo)1/(sqrt(n)sqrt(n+1))+1/(sqrt(n...

`lim_(n->oo)1/(sqrt(n)sqrt(n+1))+1/(sqrt(n)sqrt(n+2))+......+1/(sqrt(n)sqrt(4n))` is equal to

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lim_(n rarr oo) sqrt(n)/sqrt(n+1)=

lim_(n rarr oo)((sqrt(n+3)-sqrt(n+2))/(sqrt(n+2)-sqrt(n+1)))

sum_(n=1)^(oo)(1)/(sqrt(n)+sqrt(n+1))

lim_(n to oo)(1)/(n)(1+sqrt((n)/(n+1))+sqrt((n)/(n+2))+....+sqrt((n)/(4n-3))) is equal to:

lim_(n to oo)(1)/(n)(1+sqrt((n)/(n+1))+sqrt((n)/(n+2))+....+sqrt((n)/(4n-3))) is equal to:

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lim_(n rarr oo)(3+sqrt(n))/(sqrt(n))

lim _( x to oo) (1)/(sqrtn sqrt(n+1))+ (1)/(sqrtn sqrt(n+2)) is equal to :

lim_(n rarr oo)n[sqrt(n+1)-sqrt(n))]