The value of \(1+3+5+7+9+11+13+15+17+19\) is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 100
The sum of the first \(n\) odd numbers is \(n^{2}\). Here the odd numbers run from 1 to 19 without a gap.
Number of terms: 1, 3, …, 19 are the first 10 odd numbers, so \(n=10\)
Sum \(=10^{2}=100\)
Shortcut: Pair the terms from the two ends.
\(1+19=3+17=5+15=7+13=9+11=20\)
Five pairs of 20 \(=100\)