Question

tính :

B = 3+ 3/1+2 + 3/1+2+3 + 3/1+2+3+4+.....+ 3/ 1+2+3+4+..+100

Answer 1

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Answer 2

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\(\Leftrightarrow\frac{3}{\frac{1.2}{2}}+\frac{3}{\frac{2.3}{2}}+.....+\frac{3}{\frac{100.101}{2}}\)

\(\Leftrightarrow\frac{6}{1.2}+\frac{6}{2.3}+.....+\frac{6}{100.101}\)

\(\Leftrightarrow6\left(\frac{1}{1.2}+\frac{1}{2.3}+.....+\frac{1}{100.101}\right)\)

\(\Leftrightarrow6.\left(\frac{1}{1}-\frac{1}{101}\right)\)

\(\Leftrightarrow6.\frac{100}{101}=\frac{600}{101}\)

Vậy B=\(\frac{600}{101}\)