Calculate the sum of 1001 terms of the series 3,5,7,...

Expert Answers

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3, 5, 7, ...., a1001  is an A.P  such that:

a1= 3

a2= 3+ 1*2

a3= 3+ 2*2

a4= 3+  3*2

.....

a1001 = 3+ 1000*2 = 2003

r= 2

==> S1001 = 3 + 5 + 7 + ...+ a1001

 We know that:

Sn = (a1+an)*n/2

Sn = (3+ 2003)*1001/2

     = (2006)(1001)/2= 1004003.

==: Sn = 1004003

 

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