简算1/(2×3)+1/(3×4)+1/(4×5)+……+1/(18×19)+1/(19×20)
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![简算1/(2×3)+1/(3×4)+1/(4×5)+……+1/(18×19)+1/(19×20)](/uploads/image/z/45161-17-1.jpg?t=%E7%AE%80%E7%AE%971%2F%EF%BC%882%C3%973%29%2B1%2F%283%C3%974%29%2B1%2F%284%C3%975%EF%BC%89%2B%E2%80%A6%E2%80%A6%2B1%2F%EF%BC%8818%C3%9719%EF%BC%89%2B1%2F%EF%BC%8819%C3%9720%EF%BC%89)
简算1/(2×3)+1/(3×4)+1/(4×5)+……+1/(18×19)+1/(19×20)
简算1/(2×3)+1/(3×4)+1/(4×5)+……+1/(18×19)+1/(19×20)
简算1/(2×3)+1/(3×4)+1/(4×5)+……+1/(18×19)+1/(19×20)
用拆分来做
变为
1/2-1/3+1/3-1/4+...+1/19-1/20
最后中间项全部都划去了,只剩下
1/2-1/20=9/20