Question

If the sum to infinity of the series 3 + 5r +
7 r square + ... is 44/9 find r.

Answer 1

Final Answer : r = 1/4

Steps :
1) Since, series is converging,
So, | r| < 1 .


2) S = 3 + 5r + 7r^2 + ......
Th^n,
Sr = 3r + 5r^2 +7r^3 ..

Th^n,
Subtract these two
S(1-r) = 3+2r + 2r^2 + ....
S(1-r) = 3 + 2 r/(1-r)
=> S = (3-r) /(1-r) ^2
Then, see pic

Answer 2

Answer:

S = 3 + 5r + 7r^2 + 9r^3 + …..................

rS = + 3r + 5r^2 + 7r^3 + …...........

S (1 – r) = 3 + 2r + 2r^2 + 2r^3 + ….......

S (1 – r) = 3 + 2r / (1 – r)

44/9 * (1 – r)^2 = 3 – 3r + 2r

44 + 44 r^2 – 88r = 27 – 9r

44 r^2 – 79r + 14 = 0