Question

Find the partial sum for a_n = 2/(3^n)

Answer 1

Partial sum for the nth term

Answer 2

its a g.p with a=2,r=1/3

Answer 3

- partial sum for n= ?

a_1=2/3
a_2=2/9 - a_1 +a_2 =2/3 +2/9 =(6+2)/9 =8/9
a_3=2/27 - 8/9 +a_3 =8/9 +2/27 =(24+2)/27 =26/27
a_4=2/81 - 26/27 +a_4 =26/27 +2/81 =(78+2)/81 =80/81
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a_n=2/(3^n)
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- so than from these result that a_1 + ... +a_n = ((3^n) -1)/(3^n)
- hope that is understandably

- good luck

- bye !

Answer 4

how do you like it ?

Answer 5

If you start with n=1
\[s_k=3^{-k} \left(3^k-1\right)
\]
If you start with n=0
\[
s_k=3^{-k} \left(3^{k+1}-1\right)
\]