Write out the sum.
\[
\sum_{k=5}^{n}(-1)^{k} \ln k
\]
Find the first, second, third, and last terms of the sum.
\[
\sum_{k=5}^{n}(-1)^{k} \ln k=\square+\square+\square+\cdots+\square
\]
(Type an exact answer in simplified form.)
\(\boxed{\text{The first term is } -\ln 5, \text{ the second term is } \ln 6, \text{ the third term is } -\ln 7, \text{ and the last term is } (-1)^n \ln n}\)
Step 1 :Define the sum as \(\sum_{k=5}^{n}(-1)^{k} \ln k\)
Step 2 :Calculate the first term by substituting \(k = 5\) into the sum expression, which gives \(-\ln 5\)
Step 3 :Calculate the second term by substituting \(k = 6\) into the sum expression, which gives \(\ln 6\)
Step 4 :Calculate the third term by substituting \(k = 7\) into the sum expression, which gives \(-\ln 7\)
Step 5 :Calculate the last term by substituting \(k = n\) into the sum expression, which gives \((-1)^n \ln n\)
Step 6 :\(\boxed{\text{The first term is } -\ln 5, \text{ the second term is } \ln 6, \text{ the third term is } -\ln 7, \text{ and the last term is } (-1)^n \ln n}\)