1/（1×2×3×4）+3/（2×3×4×5）+5/（3×4×5×6）+7/（4×5×6×7）+……

第一步,写通式
为 (2n-1)/n(n+1)(n+2)(n+3)
第二步,在通式因子找到裂项相消的项.肯定是1/n(n+i)-1/(n+?)(n+?)
分别把i=1,2,3代入.发现得到
i=1:
1/n(n+1)-1/(n+2)(n+3)=(4n+6)/n(n+1)(n+2)(n+3) 2a+b=1 6a+4b=1
i=2:
1/n(n+2)-1/(n+1)(n+3)=(2n-4)/n(n+1)(n+2)(n+3) 6a+3b=3 6a-4b=-1
i=3:
...=2/n(n+1)(n+2)(n+3)
所以 把分子2n-1分成 (2n-4)+3/2 *2
就得到原式=∑(2n-1)/[n(n+1)(n+2)(n+3)]
=5/14∑(4n-6)/[n(n+1)(n+2)(n+3)]+2/7∑(2n-4)/[n(n+1)(n+2)(n+3)]
=5/14∑(1/n(n+1)-1/(n+2)(n+3))+2/7∑(1/n(n+2)-1/(n+1)(n+3))
=5/14*(1/(1*2)+1/(2*3)-1/(10*11)-1/(11*12))-2/7*(1/(1*3)-1/(10*12))
计算得到=39/280我是小学生，你的算式看不懂啊