find the sum of the following without actual addition . (a) 1+3+5+7+9+11+13+15+17+19
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Answer:
We have to find the sum of above series without actual addition
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 1=17
Sum of series = n2* (a + 1)
= 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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1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 +19
Total consecutive odd numbers = 10
Thus n = 10
Therefore sum = n × n
= 10× 10 = 100
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