[2024/05/18] Not a telescoping series
[2024/05/18] Not a telescoping series
It is not
2
comments
solution
Assuming the series converges it converges absolutely. Therefore
sum{n/2(n-1) | n >= 1}
= sum{(n+1)/2n | n >= 0}
= sum{n/2n | n >= 0} + sum{1/2n | n >= 0}
= sum{n/2n | n >= 0} + 2
= sum{n/2n | n >= 1} + 2=>
sum{n/2(n-1) | n >= 1} = sum{n/2n | n >= 1} + 2
=>
2 = sum{n/2(n-1) | n >= 1} - sum{n/2n | n >= 1}
= sum{n/2(n-1) - n/2n | n >= 1}
= sum{n/2n | n >= 1}
= 1/2 * sum{n/2(n-1) | n >= 1}=>
sum{n/2(n-1) | n >= 1} = 4
2Hint:
spoiler
It is not a telescoping series
Solution:
1
