Evaluate the following series.

$(a),{\displaystyle \underset{n=5}{\overset{}{}}}\frac{(-6{)}^n}{7^n}=$

$(b),{\displaystyle \underset{n=1}{\overset{}{}}}\frac{7^n}{6^n}=$

$(c),{\displaystyle \underset{n=0}{\overset{}{}}}\frac{2^n}{{10}^{2n+1}}$

$(d){\displaystyle \underset{n=2}{\overset{}{}}}\frac{1}{2^n}=1,$

$(e),{\displaystyle \underset{n=1}{\overset{}{}}}\frac{6^n+2^n}{7^n}=$

$(f),{\displaystyle \underset{n=1}{\overset{}{}}}\frac{4^n}{4^{n+4}}=$

For the series that converge, enter the sum. For the series that diverge, enter the most descriptive string, choosing from $"-$inf", "inf", and "DNE".