Show that the series is convergent using the Alternating Series Test.
\sum_(n=1)^(\infty ) ((-1)^(n+1))/(n^(4))
Identify
b_(n)
Evaluate the following limit.
\lim_(n->\infty )b_(n)
Since
\lim_(n->\infty )b_(n),0
and
b_(n+1)?b_(n)
for all
n
, the series is convergent. How many terms of the series are necessary in order to estimate the sum with an error less than 0.00005 ? terms

Question

Show that the series is convergent using the Alternating Series Test.

\sum_(n=1)^(\infty ) ((-1)^(n+1))/(n^(4))

Identify

b_(n)

Evaluate the following limit.

\lim_(n->\infty )b_(n)

Since

\lim_(n->\infty )b_(n),0

and

b_(n+1)?b_(n)

for all

n

, the series is convergent. How many terms of the series are necessary in order to estimate the sum with an error less than 0.00005 ? terms

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