1的三次方+3的三次方+5的三次方+.+99的三次方等于多少
9个回答

1的三次方+2的三次方+3的三次方+4的三次方+5的三次方+.+99的三次方

= [1/2 * 99 *(99+1) ]^2

= [1/2 * 99 *100 ]^2

= [ 99 *50 ]^2

= 4950^2

= 24502500

2的三次方+4的三次方+6的三次方+.+98的三次方

= 8*{1的三次方+2的三次方+3的三次方+.+49的三次方

= 8* [1/2 * 49 *(49+1) ]^2

= 8*[1/2 * 49 *50 ]^2

= 8*[ 49 *25 ]^2

= 8*1225^2

= 12005000

1的三次方+3的三次方+5的三次方+.+99的三次方

=【1的三次方+2的三次方+3的三次方+4的三次方+5的三次方+.+99的三次方】-【2的三次方+4的三次方+6的三次方+.+98的三次方】

= 24502500 - 12005000

= 12497500