Consider the following series. [infinity] 1 n4 n = 1 (a) Use the sum of the first 10 terms to estimate the sum of the given series. (Round the answer to six decimal places.) s10 = (b) Improve this estimate using the following inequalities with n = 10. (Round your answers to six decimal places.) sn + [infinity] f(x) dx n + 1 ≤ s ≤ sn + [infinity] f(x) dx n ≤ s ≤ (c) Using the Remainder Estimate for the Integral Test, find a value of n that will ensure that the error in the approximation s ≈ sn is less than 0.00001. n > 32 n > −32 n > 5 n > 0 n > 15

Inequality equation are those algebraic equations in which the the two equations compare with greater than sign less than sign or other inequality sign.The value of n for the given problem is,

Given-

The given series is,

Using the value of n equal to 1,2,3..... we can find the sum of ten terms with the help of above formula. Therefore,

Inequality equation are those algebraic equations in which the the two equations compare with greater than sign less than sign or other inequality sign.

Now let function,

By the inequality, we can use the formula,

For n=10, we get,

on solving the above we get,

Now by the definition of the function we can write that,

on solving it, we get,

on solving the above equation we get,

Thus the value of n for the given problem is,

For more about the inequality equation follow the link below-

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc

sina-sinb

cosb+cosa

tana-tanb

cos0+cos x pi/3

20tan

step-by-step explanation: