Carry out the following steps to show that

(a) Use the formula for the sum of a finite geometric series (11.2.3) to get an expression for

1 – x + x² – x³ + ∙ ∙ ∙ + x^2n–2 – x^2n–1

(b) Integrate the result of part (a) from 0 to 1 to get an expression for

as an integral.

(c) Deduce from part (b) that

(d) Use part (c) to show that the sum of the given series is ln 2.

Transcribed Image Text:

1 1 1.2 3.4 1 5.6 + 1 7.8 +. = In 2