Tử số = 37.101.53 - 53.101.37 = 0
=> Phân số = 0
\(\frac{3737.53-5353.37}{1^2+2^2+...+100^2}\)
\(=\frac{37.101.53-53.101.37}{1^2+2^2+..+100^2}\)
\(=\frac{0}{1^2+2^2+...+100^2}\)
\(=0\)
\(\frac{3737\cdot53-5353\cdot37}{1^2+2^2+3^2+...+100^2}\)
\(< =>\frac{198061-198061}{1\cdot1+2\cdot2+3\cdot3+...+100\cdot100}\)
\(< =>\frac{0}{1\cdot\left(2-1\right)+2\cdot\left(3-1\right)+3\cdot\left(4-1\right)+...+100\cdot\left(101-1\right)}\)
\(< =>1\cdot2-1+2\cdot3-2+3\cdot4-3+...+100\cdot101-100\)
\(< =>\left(1\cdot2+2\cdot3+3\cdot4+...+100\cdot101\right)-\left(1+2+3+...+100\right)\)
\(< =>\frac{100\cdot101\cdot102}{3}-\frac{100\cdot101}{2}\)
\(< =>343400-5050\)
\(< =>338350\)
chuc ban hoc tot nhe >.<
