Discuses the behavior of P- series.
Answers
Answer:
With p-series, if p > 1, the series will converge, or in other words, the series will add up to a specific numerical value. If 0 < p ≤ 1, the series will diverge, which means that the series won't add up to a specific numerical value.
Step-by-step explanation:
The p-series is a power series of the form or , where p is a positive real number and k is a positive integer. The p-series test determines the nature of convergence of a p-series as follows: The p-series converges if and diverges if . See more Calculus topics.
As with geometric series, a simple rule exists for determining whether a p-series is convergent or divergent. A p-series converges when p > 1 and diverges when p < 1.
1)Take 0 and store into X . ...
2) For the variable N (the current term in the series M∑N=11NP ), we go through iterations from the 1 st iteration to the M th iteration, where M is the number of terms.
3) At each iteration, add on 1NP from the previous iteration, then store the result in X , the current sum.
4) Display X .
In that case, difference between the sum of the series and the value of the integral is at most f(1). p = 1, the p-series is the harmonic series which we know diverges. When p = 2, we have the convergent series mentioned in the example above. By use of the integral test, you can determine which p-series converge.
Hope it helps!