Question

Let ( f(x)=x+2/1.3x³ + 2.4/1.35 x⁵ + 2.4 .6/1.3 .5 .7 x⁷+ ... ∀x ∈(0,1) If the value of f (1/2) is π/a√b (where a,b∈R) then |a + b| is

Answer 1

The student needs help evaluating the function f(x) at x = 1/2 and then determining the absolute sum of two constants from the expression. The full pattern of the series is needed to provide an exact answer. Mathematical understanding of sequences and series is crucial to solve the problem.

Step-by-step explanation:

The student's question is asking for assistance in evaluating a function f(x) at x = 1/2 and then determining the sum of the modulus of two constants, a and b, from the expression of the evaluated function as π/a√b. Since the provided question appears to be a part of a series or a test that may not directly align with the sequence displayed, we need to rely on our mathematical understanding of sequences and series to evaluate f(1/2).

Without the full pattern of how the series progresses in the expression for f(x), a general method would be to identify a pattern in the coefficients and exponents. Typically, power series can be expressed in a simplified form when a discernible pattern is found.

For example, the terms given can be part of a Maclaurin series for a well-known function, which when identified, could be used to find f(1/2) easily. However, without the exact series pattern, we're unable to provide an exact answer.