1²-3²+5²-7²+9²-11²+...+49²-51²
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/28 07:10:59
![1²-3²+5²-7²+9²-11²+...+49²-51²](/uploads/image/z/1127102-14-2.jpg?t=1%26%23178%3B-3%26%23178%3B%2B5%26%23178%3B-7%26%23178%3B%2B9%26%23178%3B-11%26%23178%3B%2B...%2B49%26%23178%3B-51%26%23178%3B)
1²-3²+5²-7²+9²-11²+...+49²-51²
1²-3²+5²-7²+9²-11²+...+49²-51²
1²-3²+5²-7²+9²-11²+...+49²-51²
=(1+3)(1-3)+(5+7)(5-9)+……+(49+51)(49-51)
=(1+3)×(-2)+(5+7)×(-2)+……+(49+51)×(-2)
=(1+3+5+7+……+49+51)×(-2)
=(1+51)×26/2×(-2)
=-1352
原式=(1-3)*(1+3)+(5-7)*(5+7).....+(49-51)*(49+51)
=-2*(4+12+20+....+92+100)
=-2*(4+100)*13/2
=-1352