Question

Using the limit test, determine if the following converges or diverges:
the sum of (2-(1/n))*1/7^(2n+1)

Answer 1

\[\sum \left( 2-\frac1n \right)\left( \frac17 \right)^\left( 2n+1 \right)\]

Answer 2

\[\lim_{n \to \infty} \left( 2-\frac1n \right)\times\left( \frac17 \right)^\left( 2n+1 \right)=2\times0=0\]

since this limit is 0 the sum can converge...

Answer 3

limit=0 is supposed to be inconclusive ... you might need some more work to show it actually converges

Answer 4

no, I'm sorry I only saw this until now, but its
\[\lim_{n \rightarrow \infty} (2-\frac{ 1 }{ n })*\frac{ 1 }{ 7^(2n+1) }\]
The 2n+1 is ALL an exponent of 7.

Answer 5

That is the same expression:
\[\frac{1}{7^{2n+1}}=\frac{1^{2n+1}}{7^{2n+1}}=\left(\frac{1}{7}\right)^{2n+1}\]

Answer 6

oh okay