標題:
勁深數學題 高手請入10點
發問:
(a+b+c+d+e...... +z)既2次方=咩?
最佳解答:
(a+b+c+d+......+x+y+z)(a+b+c+d+.......+x+y+z)=a(a+...+z) + b(a+....+z) + c(a+.....+z) + .....+ y(a+.....+z) + z(a+......+z)= a^2 +b^2 + c^2 + ......+ x^2 + y^2 + z^2 + 2(ab+ac+ad+ae+af+ag+ah+ai+aj+ak+al+am+an+ao+ap+aq+ar+as+at+au+av+aw+ax+ay+az+bc+bd+be+bf+bg+bh+bi+bj+bk+bl+bm+bn+bo+bp+bq+br+bs+bt+bu+bv+bw+bx+by+bz+cd+ce+cf+cg+ch+ci+cj+ck+cl+cm+cn+co+cp+cq+cr+cs+ct+cu+cv+cw+cx+cy+cz+de+df+dg+dh+di+dj+dk+dl+dm+dn+do+dp+dq+dr+ds+dt+du+dv+dw+dx+dy+dz+ef+eg+eh+ei+ej+ek+el+em+en+eo+ep+eq+er+es+et+eu+ev+ew+ex+ey+ez+fg+fh+fi+fj+fk+fl+fm+fn+fo+fp+fq+fr+fs+ft+fu+fv+fw+fx+fy+fz+gh+gi+gj+gk+gl+gm+gn+go+gp+gq+gr+gs+gt+gu+gv+gw+gx+gy+gz+hi+hj+hk+hl+hm+hn+ho+hp+hq+hr+hs+ht+hu+hv+hw+hx+hy+hz+ij+ik+il+im+in+io+ip+iq+ir+is+it+iu+iv+iw+ix+iy+iz+jk+jl+jm+jn+jo+jp+jq+jr+js+jt+ju+jv+jw+jx+jy+jz+kl+km+kn+ko+kp+kq+kr+ks+kt+ku+kv+kw+kx+ky+kz+lm+ln+lo+lp+lq+lr+ls+lt+lu+lv+lw+lx+ly+lz+mn+mo+mp+mq+mr+ms+mt+mu+mv+mw+mx+my+mz+no+np+nq+nr+ns+nt+nu+nv+nw+nx+ny+nz+op+oq+or+os+ot+ou+ov+ow+ox+oy+oz+pq+pr+ps+pt+pu+pv+pw+px+py+pz+qr+qs+qt+qu+qv+qw+qx+qy+qz+rs+rt+ru+rv+rw+rx+ry+rz+st+su+sv+sw+sx+sy+sz+tu+tv+tw+tx+ty+tz+uv+uw+ux+uy+uz+vw+vx+vy+vz+wx+wy+wz+xy+xz+yz) 2010-10-12 22:02:44 補充： To check whether this is the correct answer, we may determine the total no. of terms. In the expansion of (a+b+c+...+x+y+z)^2, it will generate 26x26 = 676 no. of terms The no. of terms of my answer = 26 + 2(25+24+....+2+1) = 26 + 2 x 325 = 676 no. of terms. Therefore my answer should be correct.
其他解答:
(a^2+b^2+c^2+d^2+e^2............+z^2)+(2ab+2cd+2ef................2yz)
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