Co-efficient of t in the expansion of, ( + p)m - 1 + ( + p)m - 2 ( + q) + ( + p)m - 3 ( + q)2 + ...... ( + q)m - 1 where - q and p q is : 1. 2. 3. 4.

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Grade 12th PassAlgebra

Co-efficient of ^t in the expansion of, ( + p)^{m - 1} + ( + p)^{m - 2} ( + q) + ( + p)^{m - 3} ( + q)² + ...... ( + q)^{m - 1}
where - q and p q is :

1.

2.

3.

4.

VISHWESH RAVI

16 Years agoGrade 12th Pass

1 Answer

Badiuddin askIITians.ismu Expert

16 Years ago

Dear VISHWESH

given series is geometric progression

find the sum of the series which is equal to

=(α +p)^m-1 [{(α +q)/(α+p)}^m -1 ] /[{(α +q)/(α+p)} -1]

simplyfy it

=[(α +q)^m -(α+p)^m]/(q-p)

now find the coeffiecient of α^t in this expression

=[^mC_t q^m-t - ^mC_t p^m-t]/(q-p)

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