Question

Calculus 2
Does the following (sequence) converge? if it does , what is the limit or explain why it converges, if it diverges explain why.
0.2, 0.24, 0.246, 0.2468, 0.24680, 0.246802

Answer 1

i would say if the pattern continues it converges to
\[\overline{.24680}\]

Answer 2

you can convert this repeating decimal to a fraction in the usual method

Answer 3

2/100 +24/100..etc?

Answer 4

no not for this one, you need
\[\frac{24680}{100,000}+\frac{24680}{100,000^2}+...\]

Answer 5

or use the old trick of writing
\[x=\overline{.24680}\\
100000x=24680\overline{.24680}\\
99999x=24680\\
x=\frac{24680}{99999}\]

Answer 6

if it converges, what is the limit?

Answer 7

that is the limit, the fraction i wrote above

Answer 8

I have never heard of this old trick though

Answer 9

We just took sequinces and series recently and I am not so good at them :(

Answer 10

then you can write it as
\[24680(\frac{1}{10^5}+\frac{1}{10^{10}}+...\] and sum the geometric sequence
same answer

Answer 11

Alright! thank you very much

Answer 12

Appreciate it

Answer 13

yw

Answer 14

\[\sum_{n=2}^{\infty} e ^{1/n}/n ^{2}\] does this series converge or diverge?