Kết quả : ( 1 + 2/3 ) x ( 1 + 2/4 ) x ( 1 + 2/5 ) x ... x ( 1 + 2/97 ) x ( 1 + 2/98 )
= ( 3/3 + 2/3 ) x ( 4/4 + 2/4 ) x ( 5/5 + 2/5 ) x .... x ( 97/97 + 3/97 ) x ( 98/98 + 2/98 )
= 5/3 x 6/4 x 7/5 x ... x 99/97 x 100/98
= ( 5 x 6 x 7 x ...x 99 x 100 ) / ( 3 x 4 x 5 x ... x 97 x 98 )
= 99 x 100 / 3 x 4
= 33 x 25 / 1 x 1
= 825
Tham khảo nha !!!
Ai nhanh và đúng nhất mình k cho.
Mình đang cần gấp!!!!!
Ta có :
\(\left(1+\frac{2}{3}\right)\left(1+\frac{2}{4}\right)\left(1+\frac{2}{5}\right).....\left(1+\frac{2}{97}\right)\left(1+\frac{2}{98}\right)\)
\(=\)\(\frac{5}{3}.\frac{6}{4}.\frac{7}{5}.....\frac{99}{97}.\frac{100}{98}\)
\(=\)\(\frac{5.6.7.....99.100}{3.4.5.....97.98}\)
\(=\)\(\frac{5.6.7.....97.98}{5.6.7.....97.98}.\frac{99.100}{3.4}\)
\(=\)\(\frac{33.25}{1.1}\)
\(=\)\(825\)
Vậy \(\left(1+\frac{2}{3}\right)\left(1+\frac{2}{4}\right)\left(1+\frac{2}{5}\right).....\left(1+\frac{2}{97}\right)\left(1+\frac{2}{98}\right)=825\)
Chúc bạn học tốt ~
\(\left(1+\frac{2}{3}\right)x\left(1+\frac{2}{4}\right)x\left(1+\frac{2}{5}\right)x.......x\left(1+\frac{2}{97}\right)x\left(1+\frac{2}{98}\right)\)
= \(\frac{5}{3}x\frac{6}{4}x\frac{7}{5}x.......x\frac{99}{97}x\frac{100}{98}\)
= \(\frac{5x6x7x......x99x100}{3x4x5x.......x97x98}\)
= \(\frac{99x100}{3x4}\)
= \(\frac{3x33x4x25}{3x4}\)
= 825
