Question

No clue on this one: "Find the sum, if it exists: 125-25+5-1+1/5..."

Answer 1

there are no notations on when the sequence terminates, just the ... at the end. I can see the sequence is being divided by -5, but...?

Answer 2

\[a= 125\]
\[r =\frac{-1}{5}\]

Answer 3

\[S = \frac{125}{1 + \frac{1}{5}}\]

Answer 4

\[S = \frac{625}{6}\]

Answer 5

i'm confused - the ... means the sequence doesn't terminate though, or?

Answer 6

\[S = \frac{a(1 -r^n)}{(1-r)}\]

Answer 7

when r<1 and n-> infinity
r^n ~0

Hence the formula becomes
\[S = \frac{a}{1-r}\]

Answer 8

\[\S_{\infty}=a1/(1-r)\] is the formula i have, so 125/1.2 = 104.167?

Answer 9

r=-1/5
so denominator becomes 1 +1/5 =6/5 = 1.2
yeah you are correct