Question

find the sum of this series.
\[\sum_{n=1}^{\infty} (-2/5)^n\]

Answer 1

start by finding the first term and common ratio

Answer 2

hmmm... common ratio: -2/5 and first term: 1?

Answer 3

you're right about common ratio = -2/5
first term is wrong

Answer 4

for the first term, plugin n = 1 :
\[a_n = \left(-\dfrac{2}{5}\right)^n\]

Answer 5

\[a_1 = \left(-\dfrac{2}{5}\right)^1 = -\dfrac{2}{5}\]

Answer 6

so both first term and common ratio are -2/5

still remember the infinite sum formula ?

Answer 7

a = -2/5
r = -2/5

plugin the values in infinite sum formula

Answer 8

it's -2/7?

Answer 9

thats right! you may use wolfram to double check
http://www.wolframalpha.com/input/?i=%5Csum_%7Bn%3D1%7D%5E%7B%5Cinfty%7D+%28-2%2F5%29%5En

Answer 10

Thank you soo much! You're amazing! :)