Question

Without doing te actual addition, find the sum of :

(i) 1+3+5+7+9+11+13+15+17+19+21+23

(ii) 1+3+5+7+9+....... +39+41

(iii) 1+3+5+7+9+........+51+53

Answer 1

(i) 1+3+5+7+9+11+13+15+17+19+21+23

= Sum of first 12 odd natural numbers

= ${12}^2=144$

(ii) 1+3+5+7+9+....... +39+41

=Sum of first 21 odd natural numbers

= ${21}^2=441$

(iii) 1+3+5+7+9+........+51+53

= Sum of first 27 odd natural numbers

= ${27}^2=729$