Page 148 - Fixtures
P. 148

@ @QSS@                      @æa@paˆ@pþàbÉà@             @

                                   [Pascal's Triangle]

                                     n

                                       .k = 0,1,…,n C(n,k)

                            C(0, 0) = 1
                                       11

                                   121
                                1331
                            14641
                         1 5 10 10 5 1
                     1 6 15 20 15 6 1
                  1 7 21 35 35 21 7 1

.
          .C(5, 3) + C(5, 4) = 10 + 5 = 15 = C(6, 4) ,

                  [The Binomial Theorem]

         x− 1     , x2 + 2y  , 3x − y  ,x +y  ,
              x2

                             :                       .

                                                 n (x + y)n
   143   144   145   146   147   148   149   150   151   152   153