Asked by Olise faith chioma
What is the sum to infinity of the series 1+7/10+(7/10)^2+(7/10)^3.....
Answers
Answer
1 + .7+ .49 + x^3 ....... .........x^oo
if x <1
sum 1+x + x^2 + x^3 .....x^oo = 1/(1-x)
here 1-x = .3
1 /.3 = 3.33............
==================
this is because
sum 1 + x^n = 1 + x + x^2 ...x^n
sum x* sum = x + x^2 + x^3....x^(n-1)
subtract
sum - x * sum = 1 - x^n
sum* (1-x) = 1-x^n
sum = (1-x^n) /(1-x) if x <1 then
sum = 1/(1-x)
if x <1
sum 1+x + x^2 + x^3 .....x^oo = 1/(1-x)
here 1-x = .3
1 /.3 = 3.33............
==================
this is because
sum 1 + x^n = 1 + x + x^2 ...x^n
sum x* sum = x + x^2 + x^3....x^(n-1)
subtract
sum - x * sum = 1 - x^n
sum* (1-x) = 1-x^n
sum = (1-x^n) /(1-x) if x <1 then
sum = 1/(1-x)
Answered by
Bot
The sum to infinity of the series is 10.