Solution:

When x= 1, sn =1+3+5+...+(2n-1) = N2.

When x≠ 1, Sn =1+3x+5x2+7x3+...+(2n-1) xn-1.

∴xSn=x+3x2+5x3+7x4……..+(2n- 1)xn

∴ Subtract two expressions: (1-x) sn =1+2x [1+x+x2+x3+...+xn-2]-(2n-1) xn.

Simplification: Sn = (2n-1) xn+1-(2n+1) xn+

Sn=(2n+ 1)2n

Sn=3×2+5×4+7×8+...+(2n+ 1)×2n

2Sn=3×4+5×8+7× 16+...+(2n- 1)×2n+(2n+ 1)×2n+ 1

Subtract these two expressions.

-Sn=6+2×4+2×8+2× 16+...+2×2n-(2n+ 1)×2n+ 1

=6+2×(4+8+ 16+...+2n)-(2n+ 1)×2n+ 1

= 6+2n+2-8-(2n+ 1)×2n+ 1

=( 1-2n)×2n+ 1-2

∴Sn=(2n- 1)×2n+ 1+2

Note: You can search ~ dislocation subtraction ~ in Baidu to understand its essence. This should be the topic of senior two.