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

Question

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

ganeshie8 · Answer

start by finding the first term and common ratio

anonymous · Answer

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

ganeshie8 · Answer

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

ganeshie8 · Answer

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

ganeshie8 · Answer

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

ganeshie8 · Answer

so both first term and common ratio are -2/5

still remember the infinite sum formula ?

ganeshie8 · Answer

a = -2/5
r = -2/5

plugin the values in infinite sum formula

anonymous · Answer

it's -2/7?

ganeshie8 · Answer

anonymous · Answer

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