Asked by ANON
Sum?
from n=3 to infinity
((2)/(n+1)-(2)/(n+3))
from n=3 to infinity
((2)/(n+1)-(2)/(n+3))
Answers
Answered by
Steve
Take a look at the first few terms in the series:
2/4 - 2/6
2/5 - 2/7
2/6 - 2/8
2/7 - 2/9
...
You can see that the terms start to cancel out. Taking the infinite sum, they all vanish except
1/4 + 2/5 = 9/10
2/4 - 2/6
2/5 - 2/7
2/6 - 2/8
2/7 - 2/9
...
You can see that the terms start to cancel out. Taking the infinite sum, they all vanish except
1/4 + 2/5 = 9/10