Question

the ratio of 3rd and 4th term of x+2/3x square

Answer 1

Check it out if i am right and if not use 3rd term as n=4 and 4th as n=5

Answer 2

Concept

A combination is a selection of items in a collection where the order of the selection does not matter.

Combination = C(n, r) = n!/r!(n–r)!

• r is the size of each permutation
• n is the size of the set from which elements are permuted
• n, r are non-negative integers
• ! is the factorial operator

T(n)=T(r+1)=(x+a)^n=C(n,r) x^(n-r) a^r

Given

For 3rd term n=4 and for 4th term n=5 is given

Find

We are asked to find the ratio of 3rd and 4th term of x+2/3x^2

Solution

For 3rd term,n=4

T(3)=T(2+1)=C(4,2) x^(4-2) (2/3x^2)^2

=6 *x^2*4/9x^4

=8/3x^2

For 4th term,n=5

T(4)=T(3+1)=C(5,3) x^(4-3) (2/3x^2)^3

=10*x*8/27 x^6

=80/27 x^5

T(3)/T(4)= (8/3x^2)/(80/27x^5)

=8 * 27 * x^5/3x^2 * 80

= (9x^3)/10

=0.9 x^3

Hence,the ratio of 3rd and 4th term is 0.9x^3

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