IIT JEE , AIEEE Forum - Mathematics , Algebra

sandeepramesh


Derive a genl expression for sum $S_{n}$ of a series with $t_{n} = (a + n \cdot b) \cdot (a + (n+1) \cdot b) \cdots (a + (n + r - 1) \cdot b)$

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EDIT!!! thought the sum was different!!!!11one

sandeepramesh

no its really easy man as i say it to be :D

proof? :)

computer001

wat is r here?? u have t_nso how does r come in?

sandeepramesh

Clearly r is a +ve number >= 1

computer001

no im askin if its like 'r runs from 1 to n' or nethin?

sandeepramesh

no a constant :)

computer001

n*r*a + {n(n+1)r/2 + nr(r-1)/2}*b ?

sandeepramesh

Can you give it as a expr involving sums of some terms?

computer001

wat do u mean??

sandeepramesh

like shrids said :)

computer001

cummon mate,u asked me to sum it up n i did,tho i aint sure..u r the genius arnd here..so y dont u bring the actual soln similar to the form i have it in n check if im rite

sandeepramesh

atleast if u post the method, it would help man! that would simplify things a lot :)

computer001

i din do much actually..
each term has a occurrin r times so each term has r*a
so total of a =n*r*a
for b:
in t_n v have b in A.P b*r/2[2n+ (r-1)1]
=b[nr + r(r-1)/2]
so total of b=b[n(n+1)r/2 + nr(r-1)/2 ]

sandeepramesh

as this sum is very very easy, only the most elegant method will be accepted

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