1/10×11+1/11×12+1/12×13+…+1/98×99+1/99×100简便运算
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![1/10×11+1/11×12+1/12×13+…+1/98×99+1/99×100简便运算](/uploads/image/z/983115-27-5.jpg?t=1%2F10%C3%9711%2B1%2F11%C3%9712%2B1%2F12%C3%9713%2B%E2%80%A6%2B1%2F98%C3%9799%2B1%2F99%C3%97100%E7%AE%80%E4%BE%BF%E8%BF%90%E7%AE%97)
1/10×11+1/11×12+1/12×13+…+1/98×99+1/99×100简便运算
1/10×11+1/11×12+1/12×13+…+1/98×99+1/99×100
简便运算
1/10×11+1/11×12+1/12×13+…+1/98×99+1/99×100简便运算
=(1/10-1/11)+(1/11-1/12)+..+(1/99-1/100)
=1/10-1/100
=9/100
原式=(1/10-1/11)+(1/11-1/12)+(1/12-1/13)+…+(1/98×-1/99)+(1/99-1/100)
=1/10-1/100=9/100
9/100