Question

2. Here you are to use the Integral Test to prove that converges, and then approximate the sum. a. Verify that the Integral Test applies. b. Apply the Integral Test. Do this by hand, and clearly state your conclusion. C. Use your calculator (or a computer) to approximate the 6th partial sum.

Answer 1

(2) (a). If Ian be a series of positive tims such that there ha continuous decreasing function fem) for which is f(n)=an for all positive intesans, nyno. Then kan onverges if and only if the impropen integral s tem da Converses Here for fi choger = the or an ano Let ung gesume a fanction f(a) = 12 for sey 1 ashich is Gulinaars and decreasing function and . Jou dans s dm me to F*T* 24. [- +]=1 = Hence Converses. integend test is valid for the above scrits.

ma The condition of Integed test applies for you to gessuming fla) = 2 ny, 1 es fa te, my, 1. This 5 a decreasing function os f)=-– co *m), 1 and we have already shown in (a). faf oo dha = 1 i 2 dn Grueges . conclude tuf Can conclude tuf & 2 is a Hence. Cue in the ar wa Convergent WO seriss.

103 Žehrysa nad Now, Si = the 6th partial sum : - the time to be =t+that that he has to 21+25+ i +10625 4.047 1027777778 =1491389 Correct up to 6 decimal places)

(4) we knew that it ran Convergers by the integerd test for a function from the area if are use the first in terms? satisfies from an < Rnk ( few da- nt S = 1491389 (Correof apte 6 d-P). He crear bounds are +<R.CZ 0 , 149 85 < R < 16 & 667 This in the required bounds of erral.