解 (2n-1)(2n+1)22n-12n+ 十 n133 ·s×. (2n-1)·(2n+ 23+23-5)+…+1(1 22n-12n+1 22n+1 ∴ lim s=lim(1 n→∞22n+ 2 级数收敛,和为解 (2 1)(2 1) 1 − + = n n  un ), 2 1 1 2 1 1 ( 2 1 + − − = n n (2 1) (2 1) 1 3 5 1 1 3 1 −  + + +  +   = n n sn  ) 2 1 1 2 1 1 ( 2 1 ) 5 1 3 1 ( 2 1 ) 3 1 (1 2 1 + − − = − + − + + n n  ), 2 1 1 (1 2 1 + = − n ) 2 1 1 (1 2 1 lim lim +  = − → → n s n n n , 2 1 = . 2 1  级数收敛, 和为