Question

Find the sum of the infinite geometric series 7+1+1/7+1/49+...

Answer 1

Answer:
Sum = 49/6

Explanation:
The geometric sequence has the following form:
a1 + a1*r + a1*r² + a1*r³ + ..... etc

The sum of the infinite geometric sequence can be computed as follows:
S = $\frac{a1}{1-r}$

1- getting r:
The given sequence is:
7 + 1 + 1/7 + 1/49 + .....
This means that:
a1 = 7
a1 * r = 1
7r = 1
r = 1/7

We can double check this value using another term:
a1 = 7
a1 * r² = 1/7
7 * r² = 1/7
r² = (1/7) / (7)
r² = 1/49
r = 1/7

2- getting the sum:
Now we have:
a1 = 7
r = 1/7

Substitute with these givens in the above equation to get the sum as follows:
S = $\frac{7}{1- 1/7r}$
S = 49/6

Hope this helps :)