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.

Answer 1

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

Answer 2

Yep.

Answer 3

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

Answer 4

Sum of 'n' terms < 0.9 sum to infinity

Answer 5

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

Answer 6

now cancel a and 1-r from both sides

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

welcome ^_^