find the sum without actually adding the following odd numbers
1. 1+3+5+7+_ _ _ +35
2. the first 99 odd numbers
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Solution
(i) 1 + 5 + 7 + ..... + 35
→ 35 = 1 + (n - 1)(2)
→ 34 = 2(n - 1)
→ 17 = n - 1
→ 18 = n
S18 = 18/2 × [2(1) + (18 - 1)(2)]
→ 9 × [2 + 34]
→ 9 × [36]
→ 324
(ii) S99 = 99/2 × [2(1) + (99 - 1)(2)]
→ 99/2 × [2 + 196]
→ 99/2 × 198
→ 99 × 99
→ 9801
Answer for (i) 324 and (ii) 9801
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