Question

1313/1212 : x = 1/1x2+1/2x3+1/3x4+1/4x5+1/5 

 

Answer 1

\(\frac{1313}{1212}:x=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5}\)

\(\frac{1313}{1212}:x=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}\)

\(\frac{1313}{1212}:x=\frac{1}{1}-\frac{1}{5}+\frac{1}{5}\)

\(\frac{1313}{1212}:x=\frac{4}{5}+\frac{1}{5}\)

\(\frac{1313}{1212}:x=1\)

\(x=\frac{1313}{1212}:1\)

\(x=\frac{13}{12}\)

Answer 2

Lời giải 

\(\frac{1313}{1212}:x=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}\)

\(\frac{1313}{1212}:x=\frac{1}{1}-\frac{1}{5}+\frac{1}{5}\)

\(\frac{1313}{1212}:x=\frac{4}{5}+\frac{1}{5}\)

\(x=\frac{1313}{1212}:1\)

\(x=\frac{13}{12}\)

Answer 3

\(\frac{1313}{1212}\)\(\div x\)\(=\)\(\frac{1}{1}\)\(-\)\(\frac{1}{2}\)\(+\)\(\frac{1}{2}\)\(-\)\(\frac{1}{3}\)\(+\)\(\frac{1}{3}\)\(-\)\(\frac{1}{4}\)\(+\)\(\frac{1}{4}\)\(-\)\(\frac{1}{5}\)\(+\)\(\frac{1}{5}\)

\(\frac{1313}{1212}\)\(\div x\)\(=\)\(\frac{1}{1}\)\(-\)\(\frac{1}{5}\)\(+\)\(\frac{1}{5}\)

\(\frac{1313}{1212}\)\(\div x\)\(=\)\(\frac{4}{5}\)\(+\)\(\frac{1}{5}\)

\(\frac{1313}{1212}\)\(\div x\)\(=\)\(1\)

\(x=\)\(\frac{1313}{1212}\)\(\div1\)

\(x=\)\(\frac{13}{12}\)