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( 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
Bài 1:
a: Tổng là:
(-19+19)+(-18+18)+...+20=20
b: Tổng là:
-18+(-17+17)+...+0=-18
Ta có \(1\frac{1}{5}x+\frac{2}{3}x=-\frac{56}{125}\)
<=> \(\frac{6}{5}x+\frac{2}{3}x=-\frac{56}{125}\)
<=> \(\frac{28}{15}x=-\frac{56}{125}\)
<=> \(x=-\frac{2}{15}\)
b) \(\frac{x+1}{99}+\frac{x+2}{98}+\frac{x+3}{97}+\frac{x+4}{96}=-4\)
<=> \(\left(\frac{x+1}{99}+1\right)+\left(\frac{x+2}{98}+1\right)+\left(\frac{x+3}{97}+1\right)+\left(\frac{x+4}{96}+1\right)=0\)
<=> \(\frac{x+100}{99}+\frac{x+100}{98}+\frac{x+100}{97}+\frac{x+100}{96}=0\)
<=> \(\left(x+100\right)\left(\frac{1}{99}+\frac{1}{98}+\frac{1}{97}+\frac{1}{96}\right)=0\)
<=> x + 100 = 0
<=> x = -100
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!!!!!
k sửa thành k
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