Monday 15 December 2014

Interesting Sums



What is interesting about the following sum?
            1+ 3 + 5 =?
             1 + 3 + 5 + 7 =?
             1 +3 + 5 + 7 + 9 =?
             1 + 3+ 5 + 7 + 9 +11 + =?
             1 + 3 + 5 + 7 + 9 + 11 + 13 =?
            1+ 3 + 5 + 7 + 9 + 11 + 13 + 15=? 
              1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 =?
              1 + 3 + 5 + 7 + ……….289 + 291+ 293 + 295 =?
             1 + 3+ 5 + 7 + 9+ 11 + 13 ……….. +R =?

Answer:  a) = 9 = 3²
                b)  = 16 = 4²
                c)  = 25 = 5²
                d)  = 36 = 6²
                e)   = 49 = 7²
                f)  = 64 = 8²
               g)  = 81 = 9²
              h)  = (291 +1)² / 2 = 21316.
               i)  = (R+ 1/ 2)²     

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