A Geometric Progression in which all terms are positive has common ratio r. The sum of first n terms is less than 90% of the sum to infinity. Show that r^n0.1.

Question

A Geometric Progression in which all terms are positive has common ratio r. The sum of first n terms is less than 90% of the sum to infinity. Show that r^n>0.1.

hartnn · Answer

know the formulas for sum of GP, finite and infinite ?

anonymous · Answer

Yep.

anonymous · Answer

I tried solving with the formulas but could not get the answer.

hartnn · Answer

Sum of 'n' terms < 0.9 sum to infinity

hartnn · Answer

a(1-r^n) / (1-r)  <0.9 a/ (1-r)

hartnn · Answer

now cancel a and 1-r from both sides

anonymous · Answer

I did it this way. 
$$a(1-r ^{n})\div( r-1) < 0.9a \div (1-r)$$

hartnn · Answer

the denominator in sum of n terms is 1-r
not r-1

hartnn · Answer

and u can cancel a and 1-r from both sides to get 
1-r^n <0.9
did u get this ?

anonymous · Answer

Oh okay. That was the mistake I was making. Thank you so much for helping! :)

hartnn · Answer

welcome ^_^