Question

for the geometric series shown, state whether the series in convergent. If the Series is convergent give its sum
9+6.3 +4.41 +...
a tutor helped me earlier but how is the sum 0.7

Answer 1

9+6.3 +4.41 +...
= 9(1 + .7 + .49 + ..
= 9(1 + .7 + .7^2 + ...)

the bracket is a geometric series with a first term of 1 and a common ration of .7

S_∞ = a/(1-r)
= 1/(1-.7)
= 1/.3
= 10/3

so the total sum is 9(10/3) = 30

Answer 2

The sum is is not 0.7. That is the ratio of successive terms.

I thought I answered the question earlier. The sum converges to 30

Answer 3

so wats 2+2