How to find the sum of:
(2+5^n)/(8^(n+1))
where n=0 and it goes to infinity.
(2+5^n)/(8^(n+1))
where n=0 and it goes to infinity.
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oo
Σ (2 + 5^n) / 8^(n+1)
n=0
Σ 2 / 8^(n+1) + Σ 5^n / 8^(n+1)
2/8 Σ 1 / 8^n + 1/8 Σ (5 / 8)^n
These are both geometric series. The first one has a ratio of 1/8, while the second has a ratio of 5/8. The first series has 1/4 as its first term. The second series has 1/8 as its first term.
(1/4) / (1 - 1/8) =
(1/4) / (7/8) = 2/7
(1/8) / (1 - 5/8) =
(1/8) / (3/8) = 1/3
2/7 + 1/3 = 13/21.
Hope this helped.
Σ (2 + 5^n) / 8^(n+1)
n=0
Σ 2 / 8^(n+1) + Σ 5^n / 8^(n+1)
2/8 Σ 1 / 8^n + 1/8 Σ (5 / 8)^n
These are both geometric series. The first one has a ratio of 1/8, while the second has a ratio of 5/8. The first series has 1/4 as its first term. The second series has 1/8 as its first term.
(1/4) / (1 - 1/8) =
(1/4) / (7/8) = 2/7
(1/8) / (1 - 5/8) =
(1/8) / (3/8) = 1/3
2/7 + 1/3 = 13/21.
Hope this helped.