March 15, math problem, please help me look at the following series of problems, ask how to do this problem, and then the famous teacher pointed out that Tianjin did not understand, please help me explain, thank you. Know the first n terms of sequence {an} and s? n？ = 1-5+9- 13+ 17-2 1+…+(- 1)? (4n-3), find s+s-s.

Solution: when n is an even number: s? n？ =( 1-5)+(9- 13)+( 17-2 1)+........+[4(n- 1)-3-(4n-3)]=-4×(n/2)=-2n

When n is odd: s? n？ =( 1-5)+(9- 13)+........+{ 4(n-2)-3-[4(n- 1)-3)]}+(4n-3)=-4×(n- 1)/2+4n-3 = 2n- 1

So s = 2×15-1= 29; s =-2×22 =-44； s = 2×3 1- 1 = 6 1；

So S+S-S=29-44+6 1=46.

Master Jin Dian: If all items are absolute values, it is 1+5+13+17+21+... This is a arithmetic progression with the first term of1and the tolerance of 4; So the term can be converted into (1-5)+(9-13)+(17-21) ... = (-4)+(-4)+ .....

There are two kinds of writing sums: even sum and odd sum. As mentioned above, when n is an even number, s? n？ =-2n； N is an odd number

What time? n？ = 2n- 1； Isn't this the sum of even terms in the formula? Is the sum of odd terms expressed by 1