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1.3+3.5+5.7+....100terms find the value of this question

1.3+3.5+5.7+....100terms find the value of this question
 

Grade:10

1 Answers

Arun
25750 Points
4 years ago
Dear student
 
3 + 3.5 + 5.7 + ...... + (2r + 1)(2r + 3)+ ....upto n terms
so, here it is clear that , 
and sum of n terms of series , 
= 
= 
we know, , means sum of square of natural number = n(n + 1)(2n + 1)/6
and  means, sum of n times of 1 i.e., 1 + 1 + 1 + 1 + 1.... n terms = n
then, Sn = 4[ n(n + 1)(2n + 1)/6 ] - n
= 2n(n + 1)(2n + 1)/3 - n
= n [ (2n + 2)(2n + 1)/3 - 1]
= n [ (4n² + 6n + 2) - 3 ]/3
= n (4n² + 6n - 1)/3
put n = 100 now
 
= 100( 40599)/3 = 1353300

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