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Calculate the sum of series 1/5, 1/5, 1/5, .... if the series contains 34 terms.
12\frac{1}{2}21
6.8
7.3
Find the sum of the infinite geometric sequence 27,18,12,8,⋯.
34
55
81
Find the sum of the terms 1/3 + 1/9 + 1/27 + ... to ∞ using the geometric sum formula?
5
−12-\frac{1}{2}−21
Complete:
The formula Sn=a1(1−rn)1−rS_n=\frac{a_1\left(1-r^n\right)}{1-r}Sn=1−ra1(1−rn) valid for ______.
r=1r=1r=1
r≠1r\ne1r=1
What is the sum of the first five terms in a geometric sequence whose 1st term is 3 and common ratio is 6?
Is the sentence true or false?
The geometric sum formula for infinite terms is given as:
If ∣r∣<1,S∞=a1−r|r|<1,S_∞=\frac{a}{1-r}∣r∣<1,S∞=1−ra .
True
False
What is the formula to calculate sum of n terms for a given geometric sequence .
Sn=a1(1−rn)1−rS_n=\frac{a_1(1-r^n)}{1-r}Sn=1−ra1(1−rn)
Sn=a1(1−rn−1)1−rS_n=\frac{a_1\left(1-r^{n-1}\right)}{1-r}Sn=1−ra1(1−rn−1)
Sn=a1(1−rn+1)1−rS_n=\frac{a_1\left(1-r^{n+1}\right)}{1-r}Sn=1−ra1(1−rn+1)
Find ∑n=110132(−2)n−1\sum_{n=1}^{10}\frac{1}{32}(-2)^{n-1}∑n=110321(−2)n−1 .
−34132-\frac{341}{32}−32341
−412-\frac{41}{2}−241
Find the sum of the first 8 terms of the geometric series if a1=1a_1=1a1=1 and r=2.
234
255
567
Find the sum of the infinite geometric sequence 8,12,18,27,⋯ if it exists.
15
does not exist
It is done.