Question

Geometric Sequence Question

Answer 1

Given Geometric Sequence : \[2, \frac{ 2 }{ 3 }, \frac{2}{9} ,...find \]
the number of terms required before the difference between the sum to infinity and the sum of the first terms is less than \[\frac{ 3 }{ 100 }\]

Answer 2

Sn - S < .03
\[\frac{1-r^n}{1-r}-\frac{1}{1-r}<.03\]
\[\frac{-r^n}{1-r}<.03\]
\[r^n<.03(r-1)\]
\[n~log(r)<log(.03(r-1))\]
\[n<\frac{log(.03(r-1))}{log(r)}\]

Answer 3

might have forgot to flip the sign due to some hidden negatives ....

Answer 4

S-Sn .... thats it :) big minus little

Answer 5

1-r instead of r-1 in the final should do it ....