find the sum of series 3^(1/2)+3+3*3^(1/2)+.... n terms

Question

anonymous · Answer

$$1+\sqrt{3}+3+3\sqrt{3}+9+9\sqrt{3}+....... infinite$$

hartnn · Answer

do you realize both of these are geometric series ?
if yes, can you tell me common ratio for both ?

anonymous · Answer

yup i realise it but as much as i remember sum of infinite series is 1/(1-r) where $$\left| r \right|\le1$$

anonymous · Answer

here r=$$\sqrt{3}$$

anonymous · Answer

and $$\sqrt{3}>1$$

hartnn · Answer

yes, so that means the sum of this series is INFINITE too!

anonymous · Answer

but do you notice that r>1 which means formula is not applicable

hartnn · Answer

yes,
when r>1 , sum is infinite when number of terms are infinite

simply because sum goes on incrasing...

anonymous · Answer

ok thats why the answer was not matching thanks by the way 
so it means answer is simply infinte

hartnn · Answer

yes!