Page 57 - Mathematics Class - XI
P. 57

TOPIC - 8:  Sequences and Series




                                                     ACTIVITY 8.1





        OBJECTIVE
        To obtain formula for the sum of squares of first n-natural numbers.

        MATERIAL REQUIRED
            Plastic unit cubes                  Nails                              Sketch pen
            Coloured papers                     Glue


        PRE-REQUISITE KNOWLEDGE
            1.  Knowledge of natural numbers                       3.  Knowledge of volume of cuboid
            2.  Knowledge of sequences


        PROCEDURE
            1.  Take 1 (= 1 ) plastic unit cube as shown in        2.  Take 4 (= 2 ) plastic unit cubes form a cuboid as
                                                                                 2
                          2
               Fig. (a).                                              shown in Fig. (b).




                                 Fig. (a)                                        Fig. (b)
            3.  Take 9 = (3 ) plastic unit cubes form a cuboid      4.  Take 16 = (4 ) plastic unit cubes form a cuboid
                          2
                                                                                   2
               as shown in Fig. (c).                                  as shown in Fig. (d).






                               Fig. (c)                                               Fig. (d)

            5.  Arrange all the cube and cuboids of Fig. (a) to (d) above so as to form an echelon type structure as shown
               in Fig. (e).



                                +                 +                      +

















                                                            Fig. (e)
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