Question

Summation from k=0 to n of [(1/k+4) - 1/(k+5)]?

Answer 1

hint:
we can write:
\[\left( {\frac{1}{4} - \frac{1}{5}} \right) + \left( {\frac{1}{5} - \frac{1}{6}} \right) + \left( {\frac{1}{6} - \frac{1}{7}} \right) + ... + \left( {\frac{1}{{n + 4}} - \frac{1}{{n + 5}}} \right) = ...?\]

Answer 2

I see how it works now.

Answer 3

hint:
so we have:
1/5 - 1/5 = 0,
-1/6 + 1/6 = 0
-1/7 + 1/7 = 0
and so on, the only 2 terms remain, namely the first one, and the last one

Answer 4

hint:
the first term is 1/4, and the last term is:
-1/(n+5)
so, what is the final result?

Answer 5

Ohh I see it now. Thank you!!

Answer 6

Thank you!!