Without adding, find the sum:
Question:

Without adding, find the sum:

(i) (1 + 3 + 5 + 7 + 9 + 11 + 13)

(ii) (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19)

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

Solution:

Sum of first $\mathrm{n}$ odd numbers $=n^{2}$

(i) $(1+3+5+7+9+11+13)=7^{2}=49$

(ii) $(1+3+5+7+9+11+13+15+17+19)=10^{2}=100$

(iii) $(1+3+5+7+9+11+13+15+17+19+21+23)=12^{2}=144$

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