Answer Happy

Use the Root Test to determine the convergence or divergence of the series.
∞
n = 1
Use the Root Test to determine the convergence or divergence of the series. n=1∑∞​(5n+1−6n​)2n Step 1 Recall the Root Test, which states that if ∑an​ is a series, and n→∞lim​n∣an​∣​<1, then ∑an​ absolutely. If n→∞lim​n∣an​∣​>1 or n→∞lim​n∣an​∣​=∞, then ∑an​ Step 2 For this series, an​=(5n+1−6n​)2n. Find n→∞lim​n∣an​∣​. n→∞lim​n∣an​∣​​=n→∞lim​n∣∣​(5n+1−6n​)2n∣∣​​=n→∞lim​(5n+16n​)2=n→∞lim​((5+6​)2​