Question

-1²+2²-3²+4²-5²+6²-7²+8²-9²+10²-11²+12²

-1²+2²-3²+4²-5²+6²-7²+8²-9²+10²-11²+12²-13²+...+30²=？

Answer 1

-1²+2²-3²+4²-5²+6²-7²+8²-9²+10²-11²+12²-13²+...+30²

= (2+1)(2-1)+(4+3)(4-3)+.......+(30+29)(30-29)

= 1+2+3+4+........................+30

= (1+30)*30/2

= 31*30/2

= 465

Answer 2

=(2²-1²)+(4²-3²)+……+(30²-29²)
=(2-1)(2+1)+(4-3)(4+3)+……+(30-29)(30+29)
=1*(2+1)+1*(4+3)+……+1*(30+29)
=1+2+3+4+……+29+30
=(1+30)+(2+29)+……+(15+16)
=31*15
=465