Tn is equivalent to the case of arithmetic multiplication of geometric series, which can be increased or decreased by the latter two formulas.

In the above example, 3Tn is to multiply each term by 3, the first term is 1×3=3, and the second term is 4×3? × 3 = 4× 3 1, and the nth ........... is

2n×3ˇ(n-2)×3=2n×3ˇ(n- 1)

So the final result is 3Tn=3+4×3ˇ 1 power +6×3ˇ2 power +...+2n× 3 ˇ (n- 1) power.

Then the two formulas are subtracted to subtract the corresponding term. Specifically, minus the idempotent term, ①-② is

Tn -3Tn=-2Tn Left sum (1+4×3? -3)+(6×3ˇ 1-4×3ˇ 1)+(8×3ˇ2-6×3ˇ2)+............+[2n×3ˇ(n-2)-2(n- 1)×3ˇ(n-2)]-2n×3ˇ(n- 1)= 2+2×3ˇ 1+2×3ˇ2+……2×3ˇ(n-2)-2n×3ˇ(n- 1)

Pay attention to the first and last items. The first few terms can be regarded as the power of 0. When subtracting the last few items, be sure to pay attention to the same number of times before subtraction. Finally, 2 is put forward and solved by geometric series formula.