High school mathematics, sequence problem, can you do this for the first small question? Isn't that enough?

Of course. Finite item verification cannot be used as the basis of the whole series.

Solution:

( 1)

When n= 1, 2a 1-a 1=a 1?

a 1(a 1- 1)=0

A 1=0 (inconsistent with the known, omitted) or a 1= 1.

Substitute A 1= 1 into the known equation and get Sn=2an- 1.

When n≥2,

an = Sn-S(n- 1)= 2an- 1-[2a(n- 1)- 1]

an=2a(n- 1)

An/a(n- 1)=2, which is a fixed value.

While a 1= 1, the sequence {an} is a geometric series with 1 as the first term and 2 as the common ratio.

an= 1 2？ =2?

The general formula of the sequence {an} is an=2?

(2)

nan = n ^ 2？

Tn= 1 1+2 2+3 2？ +...+n 2？

2Tn = 1 ^ 2+2 ^ 2？ +...+(n- 1) 2？ +n 2？

Tn-2Tn=-Tn= 1+2+...+2? -n 2？

= 1 (2? - 1)/(2- 1) -n 2？

=( 1-n) 2？ - 1

Tn=(n- 1) 2？ + 1