# Convergence of infinite series

• Apr 12th 2008, 01:46 PM
matty888
Convergence of infinite series
Investigate the convergence of the following infinite series and find their
sums, where appropriate:

i)

Hint: Find explicit expressions for the partial sums SN.

• Apr 12th 2008, 01:48 PM
Mathstud28
Quote:

Originally Posted by matty888
Investigate the convergence of the following infinite series and find their

sums, where appropriate:

i)

ii)

Hint: Find explicit expressions for the partial sums SN.

I will give you a hint...in part i there is a cancellation that can be made and in part ii and iii they are telescoping series
• Apr 12th 2008, 02:11 PM
mr fantastic
Quote:

Originally Posted by matty888
Investigate the convergence of the following infinite series and find their

sums, where appropriate:

i)

ii)
i) $\frac{2^n + 3(5^n)}{5^{n+1}} = \left(\frac{1}{5}\right) \, \left( \frac{2^n}{5^n} \right) + \frac{3}{5}$. It's the second term that will cause the series to diverge (why?)
ii) Using partial fractions: $\frac{4}{(4n-3)(4n+1)} = \frac{1}{4x-3} - \frac{1}{4x+1}$.