Binomial Q (1 Viewer)

[Watsername]

How would you go about this:

In the expansion of (3+9x)^19 determine:

a) the ratio of the cofficients of the two consecutive terms Tr , Tr+1

b)which pair of consecutive terms have equal coefficients

 

[acmilan]

You use the general formula:

T_r+1 = ¹⁹C_r 3^r (9x)^19-r

So T_r = ¹⁹C_r-1 3^r-1 (9x)^18-r

Then just divide it and youll get a)

For b) if they have equal coefficients then the ratio of T_r+1 and T_r will be 1, so use your answer from a), equate it to 1 and solve for r

 

[Watsername]

Thanks

 

[d_a_n_z]

i think it shoudl be 20 -r...rather than 18?? i dunno, did you get that its the 19c14and 19c15 terms....which are the 15th and 16th term?

 

[Antwan23q]

yeh it should be 20
because 19-(r-1)=19-r+1=20-r

 

[acmilan]

correct .