Question

2. 2 (k(ln (E))? k=2 ΣΕΠ()

Please show all work

Answer 1

Soin 2 K=2 k (In(K)? q E N K(ln(K)]² k=2 The Series can be evaluated using integral Test. .dx. a la leyle anlatmaya let In(a)=t 1 / 2 dx=dt 1 = 2. .dx x(in (x)]² lidt At t2 x=2 t=in (2) R=0 = t = ln (oo) -0. 2 ln (2) -2 t.dt -2+1 t 2+1 in (2) ر) In (2) = 2 ( t -2 In (2) in (2) -2 El In (2) - -2 intes 2 M8 2 Salon •da. = finite K[n(K)}} a ln (1) In (2) 2.885 k=2 2 the integral Converges by test. IMO K(INCk)?