SOLUTION: Write 7 Σ81(-1/3)^(k-2) k=2 in expanded form. then find the sum the sum is (182/3) i dont know how to do expanded

Algebra ->  Sequences-and-series -> SOLUTION: Write 7 Σ81(-1/3)^(k-2) k=2 in expanded form. then find the sum the sum is (182/3) i dont know how to do expanded      Log On


   

Question 1035561: Write
7
Σ81(-1/3)^(k-2)
k=2
in expanded form. then find the sum
the sum is (182/3)
i dont know how to do expanded
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

You just substitute k=2 through k=7 in the expression after  
the Σ, then add them all.

Start by substituting k=2 in
81%28-1%2F3%29%5E%282-2%29
81%28-1%2F3%29%5E%280%29+
81%281%29+
81

Substitute k=3 in
81%28-1%2F3%29%5E%283-2%29
81%28-1%2F3%29%5E1+
81%28-1%2F3%29+
-27

Substitute k=4 in
81%28-1%2F3%29%5E%284-2%29
81%28-1%2F3%29%5E2+
81%281%2F9%29+
9

Substitute k=5 in
81%28-1%2F3%29%5E%285-2%29
81%28-1%2F3%29%5E3+
81%28-1%2F27%29+
-3

Substitute k=6 in
81%28-1%2F3%29%5E%286-2%29
81%28-1%2F3%29%5E4+
81%281%2F81%29+
1

Substitute k=7 in
81%28-1%2F3%29%5E%287-2%29
81%28-1%2F3%29%5E5+
81%28-1%2F243%29+
-81%2F243
-1%2F3

Now sum them all up:

81-27%2B9-3%2B1-1%2F3
61-1%2F3
60%262%2F3
182%2F3

Edwin