How can we check that a numerical series is convergent?
There are many methods to check it, but the the most useful is: By comparison: if we find a series whose terms are greater than the given ones which is known to be convergent (an armonic series for example), then our series will be convergent too. On the other hand, if we find a series whose terms are less than the given one which is known to be divergent, then our series will be divergent.
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Related Further Mathematics IB answers
All answers ▸Use l’Hôpital’s rule to find lim(csc(x) - cot(x)) as x -> 0.
a) Given f(x) = ln(x), use the Mean Value Theorem to show that for 0 <a <b, (b-a)/b < ln(b/a) < (b-a)/a. b)Hence show that ln(1.2) lies between 1/m and 1/n, with m, n consecutive integers to be determined.
Prove that the function f:ZxZ -> ZxZ defined by f(x,y) = (2x+y,x+y) is a bijetion.
Which test for convergence is the best for which series?