Find the sum of the infinite geometric series.
4+1+1/4+....
Sum=a_1/1-r
4/1-4=?
r=a_1/a_2
r=4/1=4
a_1=4
I am stuck?Please help me.
r=1/4, a1=4, and a2=a1*r or r=a2/a1 I think that is where you went astray.
sum= 4/(1-1/4)=4/(3/4)=16/3
thank you bobpursley.
Why are you reposting the same question after it has been answered for you?
https://www.jiskha.com/questions/1770632/find-the-sum-of-the-infinite-geometric-series-4-1-1-4
This results in extra work by tutors, which should not be necessary.
To find the sum of an infinite geometric series, you can use the formula:
Sum = a_1 / (1 - r)
Where:
- Sum is the sum of the series
- a_1 is the first term of the series
- r is the common ratio
In your case, the first term (a_1) is 4, and the common ratio (r) is 1/4.
Now substitute these values into the formula:
Sum = 4 / (1 - 1/4)
To simplify the expression, you need to find a common denominator for the fraction in the denominator:
Sum = 4 / (4/4 - 1/4)
Sum = 4 / (3/4)
To divide fractions, you can multiply by the reciprocal of the second fraction:
Sum = 4 * (4/3)
Simplifying the expression further:
Sum = 16/3
So, the sum of the infinite geometric series 4 + 1 + 1/4 + ... is 16/3.