Question

The sum of the infinite series 1/5 - 2/5^2 + 2^2/5^3 - 2^3/5^4 + ...... is

Answer 1

the common ratio is -2/5, isn't it ?

Answer 2

Be smart

Answer 3

it is a geometric series, use the well known formula for it's sum

Answer 4

First term = 1/5
so sum to infinity = (1/5)/(1-(-2/5))=(1/5)/(7/5)=1/7.

Answer 5

What is the common ratio if it is GP?

Answer 6

@hartnn said it already

Answer 7

nope

Answer 8

the common ratio is -2/5, isn't it ?
that what first answer says.

Answer 9

Actually it is -2/5...why it is not ?? @Zekarias

Answer 10

\[(\frac{-2}{5})^{0}=1\]

Answer 11

Ok if the common ratio is that and the first term is 1/5 write me 1/5 in terms of -2/5

Answer 12

read what i just wrote

Answer 13

But the first term is 1/5 not 1

Answer 14

1/5*(-2/5)^0=1/5

Answer 15

WHY do u want to do that ? there is no reason to express 1/5 in terms of -2/5 to get the sum....the sum to infinity is still 1/7.....

Answer 16

=>1/5=2^0/5^1

Answer 17

correct all of you.
Thanks

Answer 18

the general term of this series is:
\[a*q ^{n}\]
where a=1/5 , q=-2/5 and n goes fomr n=0 to infinity