Question

Tính tổng A biết : A=1/1x2 + 1/2x3 + 1/3x4 + ... + 1/43x44 + 1/44x45

Answer 1

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{43.44}+\frac{1}{44.45}\)

\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{43}-\frac{1}{44}+\frac{1}{44}-\frac{1}{45}\)

\(A=\frac{1}{1}-\frac{1}{45}\)

\(A=\frac{44}{45}\)

Answer 2

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Answer 3

\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{44.45}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{44}-\frac{1}{45}\)

\(A=1-\frac{1}{45}\)

\(A=\frac{44}{45}\)