How do you determine if #Sigma (7*5^n)/6^n# from #n=[0,oo)# converge and find the sums when they exist?
Write the series as:
By signing up, you agree to our Terms of Service and Privacy Policy
To determine the convergence of the series ( \sum_{n=0}^{\infty} \frac{7 \cdot 5^n}{6^n} ), we can use the ratio test.

Apply the ratio test: ( \lim_{n \to \infty} \frac{a_{n+1}}{a_n} ) ( = \lim_{n \to \infty} \frac{7 \cdot 5^{n+1}/6^{n+1}}{7 \cdot 5^n/6^n} ) ( = \lim_{n \to \infty} \frac{5^{n+1}}{6^{n+1}} \cdot \frac{6^n}{5^n} ) ( = \lim_{n \to \infty} \frac{5}{6} ) ( = \frac{5}{6} )

Since the limit is less than 1, the series converges.
To find the sum: ( S = \frac{a}{1  r} ) ( S = \frac{7 \cdot \frac{5^0}{6^0}}{1  \frac{5}{6}} ) ( S = \frac{7}{1  \frac{5}{6}} ) ( S = \frac{7}{\frac{1}{6}} ) ( S = 42 )
Therefore, the series converges, and its sum is 42.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 How do you determine whether the sequence #a_n=(2^n+3^n)/(2^n3^n)# converges, if so how do you find the limit?
 How do you use the Ratio Test on the series #sum_(n=1)^oo(n!)/(100^n)# ?
 How do you find #lim lnt/(t1)# as #t>1# using l'Hospital's Rule?
 How do you show that the harmonic series diverges?
 Prove that lim_(n>oo) (2n+1)/(3n+2)=2/3 ?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7