4. Without actual addition, find the sum of the following
(a) 1 + 3 + 5+7
(b) 1 + 3 + 5 + 7+9+ 11 + 13
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The given series is 1+3+5+7+9+11+13+15+17
The series is in the form of AP with a=1, d=2 and n=50 and last term l=17
Sum of series = n2∗ (a + l)
= 9/2 ∗ (1+17)
= 4.5*18
=81
Therefore, answer: - the sum 1+3+5+7+9+11+13+15+17 is 81.
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