1. (a) Use the integral test to show that P[infinity] n=1 1/n4 converges. (b) Find the 10th partial sum, s10, of the series P[infinity] n=1 1/n4 . (c) According to the Remainder Estimate for the Integral Test, we know that Z [infinity] n+1 1 x 4 dx ≤ s − sn ≤ Z [infinity] n 1 x 4 dx, (1) where s is the sum of P[infinity] n=1 1/n4 and sn is the nth partial sum of P[infinity] n=1 1/n4 . Use inequality (1) and s10 from

Step-by-step explanation:

a)

Substitute limits to get

=

Thus converges.

b) 10th partial sum =

=

c) Z [infinity] n+1 1 /x ^4 dx ≤ s − sn ≤ Z [infinity] n 1 /x^ 4 dx, (1)

where s is the sum of P[infinity] n=1 1/n4 and sn is the nth partial sum of P[infinity] n=1 1/n4 .

(question is not clear)

x^6

step-by-step explanation:

this is correct because:

x-6=0

0*x=0

so

x^6

add all the numbers and check the ones place.

the answer is 486. as the ones place is more than 4, the estimation will be the next 10 ie, 490