In this question, well practice using the direct comparison test.Drop-down menus cant display formatted math, so you should interpret =1 r <1), the series i=9

In this question, well practice using the direct comparison test.Drop-down menus cant display formatted math, so you should interpret <= as , etc.1. we would like to determine the convergence or divergence of i=91i4. Your comparison for this part will be chosen from the list below.a(i)=1ib(i)=1i2c(i)=15d(i)=14i2For all sufficiently large i,1i4?<>? a(i) b(i) c(i) d(i), and both have nonnegative terms.By ? the p-test geometric series test (with ? p<=1 p>1 r>=1 r<1), the series i=9 ? a(i) b(i) c(i) d(i)? converges diverges .So, we conclude i=91i4? converges diverges as well, by the direct comparison test.2. We would like to determine the convergence or divergence of i=11i2+4. Your comparison for this part will be chosen from the list below.a(i)=1ib(i)=1i2c(i)=15d(i)=14i2For all sufficiently large i,1i2+4?<>? a(i) b(i) c(i) d(i), and both have nonnegative terms.By ? the p-test geometric series test (with ? p<=1 p>1 r>=1 r<1), the series i=1 ? a(i) b(i) c(i) d(i)? converges diverges .So, we conclude the series i=11i2+4? converges diverges as well, by the direct comparison test.3. We would like to determine the convergence or divergence of i=1(1/5)ii+6. Your comparison for this part will be chosen from the list below.a(i)=16b(i)=15c(i)=1i+6d(i)=(15)iFor all sufficiently large i,(1/5)ii+6?<>? a(i) b(i) c(i) d(i), and both have nonnegative terms.By ? the p-test geometric series test (with ? p<=1 p>1 r>=1 r<1), the series i=1 ? a(i) b(i) c(i) d(i)? converges diverges .So, we conclude the series i=1(1/5)ii+6? converges diverges as well, by the direct comparison test.4. We would like to determine the convergence or divergence of i=12i3+9i2+6i+1i5+3xi100i. Your comparison for this part will be chosen from the list below.a(i)=1ib(i)=1i2c(i)=1i3d(i)=1i4For sufficiently large i,2i3+9i2+6i+1i5+3xi100i ?<>? a(i) b(i) c(i) d(i), and both have nonnegative terms.By ? the p-test geometric series test (with ? p<=1 p>1 r>=1 r<1), the series i=1 ? a(i) b(i) c(i) d(i)? converges diverges .So, we conclude the series i=12i3+9i2+6i+1i5+3xi100i ? converges diverges as well, by the direct comparison test.