Question

find if the seq converges or diverges {(-1)^n (n+5/5^n)}

Answer 1

let \( a_n \) be the n-th element of the sequence.
show that \[
i) \lim_{n \rightarrow \infty} a_n = 0 \]

Answer 2

i found first term -6/5 second term -23/25 and the third term as -123/125 but i don't any relationship btw them

Answer 3

you don't need relationship between them to show that the sequence converges.
just show that as \( n \rightarrow \infty \) the value if the n-th term is zero.
In other words, show that
\[ \lim_{n\rightarrow \infty} {(-1)^n (n+5) \over 5^n} = 0\]

Answer 4

If,
\[ \lim_{n\rightarrow \infty} {(-1)^n (n+5) \over 5^n} = \infty (\text{ the series diverges} )\]
\[ \lim_{n\rightarrow \infty} {(-1)^n (n+5) \over 5^n} = a \text{ (for some value 'a', then the series converges})\]

Answer 5

thx

Answer 6

sorry, *sequence .. not series

Answer 7

with the limit to infinity can you take out (1/5)^n

Answer 8

use L'Hopital rule

Answer 9

ok

Answer 10

how do u d/dx 5^n

Answer 11

or (-1)^n

Answer 12

your variable is 'n' not 'x'
\[ {d \over dn} (5^n) = {d \over dn} (e^{n\ln 5})\]
you should be able to do it.
for (-1)^n, don't bother, just ignore it. If you want to do it then use power rule.