a(n)=2002×( 1/2)^(n- 1)

∴T(n)=a 1a2a3……an

=(2002^n)[( 1/2)^(0+ 1+2+……+n- 1)]

=(2002^n)×( 1/2)^[n(n- 1)/2]

Let T(k) be the maximum, then T(k)≥T(k+ 1), and T(k)≥T(k- 1).

Abel summation formula

This formula, also known as the partial sum formula, is a formula for discrete integration by parts, which was first proposed by mathematician Abel. This method is also suitable for solving the sum of multiplication series of arithmetic equal ratio series, but compared with the above dislocation subtraction, this method is convenient, fast and easy to prove. You can write the proof process first, and then substitute the exam directly into the formula.