Question

test the convergence or divergence, sum (n=0..inf)(1/2n-1/2n+6)

Answer 1

help me answer this questions

Answer 2

\[\sum_{1}^{\infty}\frac{ 1 }{ 2n }-\frac{ 1 }{ 2n+6 }=\frac{ 1 }{ 2 }\sum_{1}^{\infty}\frac{ 1 }{ n }-\frac{ 1 }{ n+3 }=\\\frac{ 1 }{ 2 }\sum_{1}^{\infty}\frac{ 1 }{ n }-\frac{ 1 }{ n+1 }+\frac{ 1 }{ n+1 }-\frac{ 1 }{ n+2 }+\frac{ 1 }{ n+2 }-\frac{ 1 }{ n+3 }=\]

Answer 3

now you have 3 sum in form of
f(n)-f(n+1)
so now
put n=1,2,3,...
simplify
you will see it converge

Answer 4

ouw....thank you...

Answer 5

understand it ?

Answer 6

yes....

Answer 7

the equation is telescoping series right?