IIT JEE , AIEEE Forum - Mathematics , Algebra - sequence and series doubt -->;

anchitsaini

If

and

then find

_{[ r =1 ]}

^{[ n ]}

(please give complete solution)

EDIT -->

Ans -- > (n+1)² * f(n+1) - (n² + 3n + 2) / 2

arpan1

is the ans 2

anchitsaini

huh?
how can u get an answer without getting "n" in it ???

arpan1

i assumed n = infinity

anchitsaini

what a great assumption !!!!

please solve it using n as a finite quantity

arpan1

see why dont u do it urself using limit of sum method !!!

anchitsaini

arey do it naa yaar

i am not as intelligent as you are
thats why i am having a problem !!

hsbhatt

Do u get (n+1)²

1/r - n(n+1)/2

anchitsaini

sir the ans given is

(n+1)^2 * f(n+1) - (n^2 + 3n + 2) / 2

arpan1

_{[r=1 ]}

^{[n ]} 2r . f(r) + _{[r=1 ]}

^{[n ]} f(r)

=( n (n+1) + 1 ) _{[r=1 ]}

^{[n ]} f(r)

now as far as i know , f(r) forms an h.p. whose sum cannot be evaluated

anchitsaini

arpan try to match your answer with the answer i gave

hsbhatt

@anchit: the two answers are equivalent

(n+1)²f(n+1) - (n+1)(n+2)/2 = (n+1)²f(n) + (n+1) - (n+1)(n+2)/2 = (n+1)²f(n) - n(n+1)/2

arpan1

@ ACHIT

if u want, i will do it

anchitsaini

ok sir

i didn't try matching it

pls give the soln