Question

Sum of first 100 odd numbers 1,3,5,....... is 10000.How much is the sum of 100 odd numbers starting from 21?​

Answer 1

$\: (1+199)+(3+197)+⋯+(99+101)=50×200=10,000(1+199)+(3+197)+⋯+(99+101)=50×200=10,000</p><p></p><p>Or</p><p></p><p>∑n=1N(2n−1)=2∑n=1Nn−N=N(N+1)−N=N2∑n=1N(2n−1)=2∑n=1Nn−N=N(N+1)−N=N2</p><p></p><p>Which, for N=100N=100, is 100×100=10,000100×100=10,000.</p><p></p><p>Or, I guess, you could just add up the odd numbers…</p><p></p><p>$