Question

A=1/2.5+1/5.8+1/8.11+.....+1/92.95+1/95.98

A=?

Answer 1

\(A=\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{95.98}\)

\(A=\frac{1}{3}\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{95.98}\right)\)

\(A=\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{95}-\frac{1}{98}\right)\)

\(A=\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{98}\right)\)

\(A=\frac{1}{3}\cdot\frac{24}{49}=\frac{8}{49}\)

Answer 2

\(=3.\left(\frac{3}{2.5}+\frac{3}{5.8}+...+\frac{3}{95.98}\right)\)

\(=3.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{95}-\frac{1}{98}\right)\)

\(=3.\left(\frac{1}{2}-\frac{1}{98}\right)\)

\(=3.\frac{24}{49}\)

\(=\frac{72}{49}\)

Answer 3

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Answer 4

A=2⋅51​+5⋅81​+8⋅111​+...+92⋅951​+95⋅981​

⇒3�=3(12⋅5+15⋅8+18⋅11+...+192⋅95+195⋅98)⇒3A=3(2⋅51​+5⋅81​+8⋅111​+...+92⋅951​+95⋅981​)

⇒3�=32⋅5+35⋅8+38⋅11+...+392⋅95+395⋅98⇒3A=2⋅53​+5⋅83​+8⋅113​+...+92⋅953​+95⋅983​

⇒3�=12−15+15−18+18−111+...+192−195+195−198⇒3A=21​−51​+51​−81​+81​−111​+...+921​−951​+951​−981​

⇒3�=12−198⇒3A=21​−981​

⇒3�=2449⇒3A=4924​

⇒�=2449:3⇒A=4924​:3

⇒�=849⇒A=498​

Vậy �=849A=498​