Question

pls help... T^T

Answer 1

hi,
which one have you tried ?

Answer 2

actually, i dont understand the qn.. are we supposed to find the 1/n^p coz i just basically compared.. like for the 1st eqn, it diverges. since 1/n diverges, so they match? is it like that?

Answer 3

i don't know the exact method to find 'p'
but since the choices are given, it makes it easier,
like if i take first one,
lim of [sqrt{n^1+1} -n] /n
would give you a positive real number
and not

lim of [sqrt{n^1+1} -n] /n^2
or
lim of [sqrt{n^1+1} -n] /n^3

its like checking each option against the question.
not a preferable method thought, but in the end it will lead you to correct answers

Answer 4

oh.. okay i'll try that.. actually, i've tried many time and ive got this feedback.

Answer 5

im just wondering why do we need to calculate a total of 24 limits?

Answer 6

oh haha! even that say we should try all possible combinations!

like try 1/n with first question, then 1/n^2 , then 1/n^3 and then as it is.
same for 2nd, 3rd , 4th question
thats why 24 limits

Answer 7

oh.. wth.. haha, omg.. okay, so the goal is to only see which gives a positive number.

Answer 8

yeah

Answer 9

know how to calculate those limits ?

Answer 10

yeah i think i only get positive value on the 1st eqn for 1/n

Answer 11

thats correct

Answer 12

isnt it like this? \[\lim_{n \rightarrow \infty} \frac{ \sqrt{n^2+1}-1 }{ n } = 1\]

Answer 13

yeah so wht does tht mean? the rest is no p-series is compatible with?

Answer 14

so you got D for first one.
try B (1/n^2) for 2nd one

Answer 15

why D for the 1st one?

Answer 16

i thought ist C?

Answer 17

yeah, yeah, i meant C sorry,

Answer 18

ohh so 2nd eqn is B coz i got 1/2 isit correct?

Answer 19

but for 1/n^3 i got infinity for the 2nd eqn what does tht mean?

Answer 20

it means 1/p^3 is not the correct p series for 2nd

for 1/p^2 , since you got positive real number for 2nd, 1/p^2 is correct one for 2nd

Answer 21

try 1/n^3 for 3rd

Answer 22

i got 1/2 for 3rd part , so means 3rd eqn is 1/n^3 ?

Answer 23

yes,
for 3rd one , correct p series is 1/p^3

Answer 24

the last one is 0 so no p-series?

Answer 25

yeah, thats the only option left to choose anyways :P

Answer 26

WOW!!! atlast.. thanks alot! you're a very big help! xD

Answer 27

you're welcome ^_^
always happy to help :)