\(\frac{3}{2^2}\)+\(\frac{5}{6^2}\)+\(\frac{7}{12^2}\)+ ....+\(\frac{19}{90^2}\)
= \(\frac{3}{4}\)+\(\frac{5}{36}\)+\(\frac{7}{144}\)+....+\(\frac{19}{8100}\)
= (\(\frac{3}{4}\)+\(\frac{5}{36}\)+\(\frac{7}{144}\)) + .... \(\frac{19}{8100}\)
= (\(\frac{108}{144}\)+\(\frac{20}{144}\)+\(\frac{7}{144}\)) +....+\(\frac{19}{8100}\)
= \(\frac{108+20+7}{144}\)+....+\(\frac{19}{8100}\)
=\(\frac{135}{144}\)+....+\(\frac{19}{8100}\)
=\(\frac{7593,75}{8100}\)+....+\(\frac{19}{8100}\)
=\(\frac{7593,75}{8100}\)+\(\frac{19}{8100}\)
=\(\frac{7593,75+19}{8100}\)
=\(\frac{7612,75}{8100}\)
mik không chắc đúng không?
=3/4+5/36+......+19/8100
=3/1.4+5/4.9+.............+19/81.100
=1/1-1/4+1/4-1/9+...............+1/81-1/90
=1/1-1/90=1-1/90=89/90
\(\frac{3}{2^2}+\frac{5}{6^2}+\frac{7}{12^2}+...+\frac{19}{90^2}\)
= \(\frac{3}{2^2}\)+ \(\frac{5}{2^2.3^2}\)+\(\frac{7}{2^2.6^2}\)+ .... + \(\frac{19}{2^2.45^2}\)
=\(\frac{3}{2^2}\)+\(\frac{5}{2^2}\)-\(\frac{5}{3^2}\)+ \(\frac{7}{2^2}\)-\(\frac{7}{6^2}\)+ .... +\(\frac{19}{2^2}\)-\(\frac{9}{45^2}\)
=\(\frac{3+5+7+9+11+13+15+17+19}{2^2}\)-(tự làm)
= \(\frac{99}{4}\)-(tự làm)
