Tính a. S= 1.3+3.5+5.7+…..+97.99 b. S=1.3.5+3.5.7+5.7.9+….+95.97.99 c. S=1.2+3.4+5.6+7.8+……+99.100 d. S=1.2.3+3.4.5+5.6.7+…+99.100.101

0 bình luận về “Tính a. S= 1.3+3.5+5.7+…..+97.99 b. S=1.3.5+3.5.7+5.7.9+….+95.97.99 c. S=1.2+3.4+5.6+7.8+……+99.100 d. S=1.2.3+3.4.5+5.6.7+…+99.100.101”

1. Đáp án:

    

   Giải thích các bước giải:

     a)   ta có S=1(1+2)+3(2+3)+5(2+5)+…+97(97+2)+99(99+2)

                     S=1*1+1*2+3*2+3*3+…+97*97+97*2+99*99+99*2

                      S= (1^2+3^2+5^2 +…+97^2+99^2)+2(1+3+5+…+99)

                       S=166650+2*2500

                        S= 171650

   D)  S= 9*10*11*12/4=2970

   B)  ta có    s= 1*3*5+3*5*7+5*7*9+…+95*97*99

   =>8S = 1.3.5.8 + 3.5.7.8 + 5.7.9.8 + … + 95.97.99.8

             = 1.3.5(7 + 1) + 3.5.7(9 – 1) + 5.7.9(11 – 3) +… +95.97.99(101 – 93)

             = 1.3.5.7 + 15 + 3.5.7.9 – 1.3.5.7 + 5.7.9.11 – 3.5.7.9 + …+ 95.97.99.101 – 93.95.97.99

             = 15 + 95.97.99.101

   => 8s=15 + 92140785=92140800

   =>  8s = 92140800

          s= 11517600

   c) 3s= 1*2*3+3*4(5-2) + 5 . 6 . ( 7 – 4 ) +…..+ 99 . 100 . (101 – 98 )

   3s = 1. 2 . 3 + 3. 4 . 5 – 2 . 3 . 4 + 5 . 6 . 7 – 4 . 5 . 6 +…..+ 99 . 100 . 101 – 98 . 99 . 100

   3s = 1 . 2 . 3 + 99 . 100. 101

    3s = 3 . 2 + 3 . 33 . 100 . 101

   3s = 3 ( 2 + 333 300)

   =>s = 3 . 333 302 : 3

   => s = 333 302

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2. Bài làm :

   `6S=1.3.6 + 3.5.6 + 5.7.6 + … + 97.99.6`

   `=1.3(5+1) + 3.5(7-1) + 5.7(9-3) + … + 97.99(101-95)`

   `=1.3.5 + 1.3 + 3.5.7 – 1.3.5 + 5.7.9 – 3.5.7 + … + 97.99.101 – 95.97.99`

   `=1.3.5 + 3 + 3.5.7 – 1.3.5 + 5.7.9 – 3.5.7+ … + 97.99.101 – 97.97.99`

   `=3+97.99.101`

   `⇒S=(3+97.99.101)/6`

   `S=161651`

   `8S=1.3.5.8 + 3.5.7.8 + 5.7.9.8 + … + 95.97.99.8`
   `= 1.3.5(7 + 1) + 3.5.7(9 – 1) + 5.7.9(11 – 3) + … + 95.97.99(101 – 93)`
   `= 1.3.5.7 + 15 + 3.5.7.9 – 1.3.5.7 + 5.7.9.11 – 3.5.7.9 + … + 95.97.99.101 – 93.95.97.99`
   `= 15 + 95.97.99.101`

   `⇒S=(15 + 95.97.99.101)/8`

   `S=11517600`

   ` S= (2 – 1).2 + (4 – 1).4 + (6 – 1).6 + … + (100 – 1).100`

   `= 2^2 – 2 + 4^2 – 4 + 6^2 – 6 + … + 100^2 – 100`

   `= (2^2 + 4^2 + 6^2 + … + 100^2) – (2 + 4 + 6 + … + 100)`

   `= 2^2.(1^2 + 2^2 + 3^2 + … + 50^2) – (100 + 2).50/2` ( kết quả câu trên)

   `⇒=(22.50.51.52 )/6 – 51.50`

   `S= 85850`

   `S = 1.2.3+3.4.5+5.6.7+…+99.100.101`

   ` = 1.3 (5-3) + 3.5 (7-3) + 5.7 (9-3) + ………… + 99.101 (103 – 3)`

   ` = (1.3.5 + 3.5.7 + 5.7.9 + ………. + 99.101.103) – (1.3.3 + 3.5.3 + ……. + 99.101.3)`

   `= (15+99.101.103.105/8 – 3.(1.3 + 3.5 +5.7 + …… + 99.101)`
   `⇒S = 13517400 – 3.171650` (kết quả câu đầu)
   `S= 13002450`

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