Q. 253.9( 22 Votes )

Find the sum of the following series up to n terms:


Answer :

The nth term of series is



Now, first solve the numerator & denominator separately


13 + 23 + 33 + … + n3 …(1)


Also,


1 + 3 + 5 + … + n terms


This is an AP.


whose first term(a) =1 & common difference(d) = 3 - 1 = 2


Now, sum of n terms of AP is


Sn = (n/2)[2a + (n - 1)d]


= (n/2)[2(1) + (n - 1)2]


= (n/2)[2 + 2n - 2]


= (n/2)[2n]


= n2


Sn = n2 …(2)


Now,



putting values from (1) & (2)






Now, Finding Sum of n terms of Series













Thus, the required sum is


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