find the sum of the series 1 by 1 by 3 + 1 by 9 by 1 by 27 +
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Answer:
S∞=1/2
Explanation:
Formula for sum of infinite geometric series is
S∞=a1/1−r; −1<r<1
We have a geometric series :
1/3+1/9+1/81+.........
First we know
a1=1/3(the first term)
Second: Identify r ,
we know r=a2/a1 or r=an/an−1
r=1/9/1/3 ⇔1/9⋅3/1=1/3
r=1/3
Substitute into the formula
S∞=1/3/1−1/3=1/3/2/3=(1/3)⋅(3/2)
S∞=1/2
S∞=1/2
Explanation:
Formula for sum of infinite geometric series is
S∞=a1/1−r; −1<r<1
We have a geometric series :
1/3+1/9+1/81+.........
First we know
a1=1/3(the first term)
Second: Identify r ,
we know r=a2/a1 or r=an/an−1
r=1/9/1/3 ⇔1/9⋅3/1=1/3
r=1/3
Substitute into the formula
S∞=1/3/1−1/3=1/3/2/3=(1/3)⋅(3/2)
S∞=1/2
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