I will be using the ratio test to prove `sum_(n=1)^oo6^n/7^n`
is absolutely convergent => the serie converge =>`sum_(n=5)^oo6^n/7^n`
Let's rewrite the serie first. `sum_(n=5)^oo6^n/7^n=sum_(n=5)^oo(6/7)^n`
Please note that in the convergence test we look at the limit of the absolute value of the ratio of the n+1 term to the n term. But sinve both of our terms are positive, we will not need them.
Hence the serie absolutely converge => the serie converge.