Question

supose if we have 100 as an index in the( 2a3d) in the given equation then how can we find the the coefficient of that in a very simple method?

Answer 1

$\huge{Hey Mate!!!}$

☆☞ Here is ur answer ☜☆

☆☞ Using Binomial theorem, we have:

(2a + 3d)100 =100C0 (2a)100 +100C1(2a)100–1 (3d) + 100C2 (2a)100–2(3d)2 + _ _ _ _ _ + 100C100–1 (2a) (3d)100–1 + 100C100 (3d)100

= (2a)100 +100 (2a)99 (3d) + 4950 (2a)98 (3d)2 + _ _ _ _ _ + 100 (2a) (3d)99 + (3d)100

☆☞ The general term of this Binomial expansion is given by,

Tr+1 = 100Cr (2a)100 – r (3d)r

☆☞ You have not mentioned the term whose coefficient you need. Write your question in detail and do get back to us so that we can provide you a meaningful help.


HOPE IT HELPS!!!

Answer 2

Using Binomial theorem, we have:

(2a + 3d)100 =100C0 (2a)100 +100C1(2a)100–1 (3d) + 100C2 (2a)100–2(3d)2 + _ _ _ _ _ + 100C100–1 (2a) (3d)100–1 + 100C100 (3d)100

= (2a)100 +100 (2a)99 (3d) + 4950 (2a)98 (3d)2 + _ _ _ _ _ + 100 (2a) (3d)99 + (3d)100

☆☞ The general term of this Binomial expansion is given by,

Tr+1 = 100Cr (2a)100 – r (3d)r

☆☞ You have not mentioned the term whose coefficient you need. Write your question in detail and do get back to us so that we can provide you a meaningful help.