 19  1-13  , , , , 36 , 2026
 


  -2026      ..

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 19  1-13  , , , , 36 , 2026





 1






19 - 1 - 2026

    .         *,   k ,  5      .        ,   k+2    5      . ,      150,   160 ,     100,   120 .

1)   k   3?

2)           ?

)           ?

*    ()   , .

.

 S -      , )  k = 3.

    , S   ,  1503  5 = 445  ,  1603  5 = 475.

    , S   ,  1005  5 = 495  ,  12055= 595.

,  S     495   475. , k     3.

2)     ), k     1 ( S     295   155)  k     2 ( S     395   315).   = 4, ,    , S   ,  1504  5= 595,  ,  1604  5 = 635;     , S  ,  1006  5 = 595,  ,  1206  5 = 715.,   = 4 ,  596 < S < 634.    , ,  S + 5    k,  k+2.  ,   4,  6   [601; 639],  612., S = 607     153 ,     102.

3) ,  k > =8,   k=  + 8 ,   > =0 .,    , S   ,  150( + 8)  5 = 1195 + 150  ,  160( + 8) - 5 = 1275 + 160. ,    , S   ,  100( + 10) 5 = 995 +100  ,  120( + 10) 5= 1195 + 120. ,  1195 +150 < S < 1195 + 120,   < 0. , k <= 7.

 k = 7.    , S   ,  1507  5 = 1045,  ,  1607  5 = 1115;     , S   ,  1009  5 = 895,  ,  1209  5 = 1075. ,  k = 7 ,  1046 <= S <= 1074.     , ,  S + 5    k,  k + 2 .  ,   7,  9   [1051;1079],  1071.

, S = 1066     153 ,     119.

: ) ; ) 607; ) 1066.




 2


19-2-2026

     .         *   k ,  7      .        ,   k + 3    7      . ,      160,   170 ,    -  100,   120 .

)   k   4?

)           ?

)           ?

  -   ,

 -     ,  b      .   :

1. n = k7. 2.  = b(k + 3)7. 3. 160 < B < 170. 4. 100 < b < 120.

    :

kB7=b(k+3)7 =>B=(1+3/k)b.

1.   k = 4:

 k = 4,   = (1 + 3/4)  b = 1,75b.

     :

 b = 101,   = 1,75  101 = 176,75 (  170).

 b > 100,      1,75 100 = 175.    . , k     4.

2.    k.

  : B/b = 1 + 3/k.      max:

Bmax/bmin =169/101 = 


1,673; Bmin/bmax = 161/119 =


 1,353=>1,353< 1+3/k <1,673   k: 3/k < 0,673 => k > 4,45; 3/k > 0,353, k <8,5 => k = 5,6,7,8.

      k,    b  B,    = b(k+3)/k = 5 => B=1,6b.  b=105,   = 168 ().   = 5  168  7 = 833.

  k= 6,  = 1,5b.  b = 108,   = 162 => n = 6162  7 = 965;  b = 110,   = 165.   = 6  165 7 = 983;  b = 112,   = 168,   = 6  168  7 = 1001.

 k= 7: =10B/7 => b  7.  b = 112,   = 160 (   > 160).  b = 119,   = 170 (  ,  < 170).  k = 8: B=11b/8,  B ,  , b  8.  b = 112,  B = 154 ().   8   (100;120) .     833 (k=5),   1001 (k=6).

: ) ; ) 833; ) 1001.






 3


19-3-2026

  60    ,                . )          400?  )         400? )         ?

   60      (      )      :            : 1.  .         ,          (            ,    ). ,         .  ,     ,      .

2. ( )     - 400?

, .   ,   .

 a1 =  400, 2 =  399 => 1 + 2 =  799.           ,              .     : a60 =  131, a59=  132,... , 55 =  136.

   : (  131) + ( 132) + ( 133) + (  134) + ( 135) + ( 136) =

= 801.

  799 >  801 . ,  400    . 3. ( )     400?

, .   ,        ( , a60).




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   .

   ,     (https://www.litres.ru/book/sergey-voronov-33860/reshenie-19-zadach-1-13-varianty-ege-matematika-profi-74232082/)  .

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