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B = 999999 * 1999 + 1999
B = 999999 * 1999 + 1999 * 1
B = 1999 * (999999 + 1)
B = 1999 * 1000000
B = 1999000000
~Study well~
#SJ
B=999999.1999+1999
= 1999.(999999+1)
=1999.1000000
=1999000000
#hok tốt#
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cl: (số cuối + số đầu) nhân ss hạng rồi chia 2
(999999+1)*999999/2 =4999995
Ta có quy tắc tỉnh tổng các số tự nhiên liên tiếp từ 1 là
\(\frac{n\left(n+1\right)}{2}=\frac{999999\left(999999+1\right)}{2}=\frac{999999.1000000}{2}=499999500000\)
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\(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}\)
\(=\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)
\(=13.\left(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}\right)\)
\(=13.\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\right)\)
\(=13.\)\(\frac{1}{2}.\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)
\(=\frac{13}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-...-\frac{1}{11}\right)\)
\(=\frac{13}{2}.\left(\frac{1}{3}-\frac{1}{11}\right)\)
\(=\frac{13}{2}.\frac{8}{33}\)
\(=\frac{52}{33}\)
!
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= 13/15 + 13/35 + 13/63 + 13/99
= 13/ 3×5 + 13/5×7 + 13/7×9 + 13/9×11
= 13 x 1/2( 1/3 – 1/5 + 1/5 – 1/7 +1/7 – 1/9 +1/9 – 1/11)
= 13/2 x ( 1/3 – 1/11)
= 13/2 x 8/33 = 104/66=52/33
\(D=\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)
\(D=\frac{13}{3}\times5+\frac{13}{5}\times7+\frac{13}{7}\times9+\frac{13}{9}\times11\)
\(D=13\times\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)
\(D=\frac{13}{2}\times\left(\frac{1}{3}-\frac{1}{11}\right)\)
\(D=\frac{13}{2}\times\frac{8}{33}=\frac{104}{66}=\frac{52}{33}\)
\(D=\frac{52}{33}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
(131313/151515+ 131313/353535+131313/636363+131313/999999)*33
=(13/15+13/35+13/63+13/99)*33
=52/33*33
=52
![](https://rs.olm.vn/images/avt/0.png?1311)
Số số hạng là:
( 999999 - 1 ) : 1 + 1 = 999999 ( số hạng )
Tổng là:
( 999999 + 1 ) x 999999 : 2 = 499999500000
Đ/S: 499999500000
333+333=666
453535+5576475=6030010
790+999999=1000789