the value of summation r=0 to r=m of 10Cr20Cm-r is maximum when: 5 10 15 20 - Maths - Binomial Theorem

Question

the value of summation r=0 to r=m of 10Cr
20Cm-r is maximum when:

5
10
15
20

Rahul Raj · Accepted Answer

Dear student

(1+x)20=C020+C120x+ +C2020x20(1+1/x)10=C010+C110(1/x)+
+C10101/x10given summation= coefficient of xr in (1+1/x)10 ×  coefficient of xm-r in (1+x)20=coefficient of xm in (1+x)20(1+1/x)10=coefficient of xm in (1+x)30x10=coefficient of xm+10 in (1+x)30 =Cm+1030
which is maximum when m=20

Regards

the value of summation r=0 to r=m of 10Cr 20Cm-r is maximum when: 5 10 15 20

the value of summation r=0 to r=m of ¹⁰C_r ²⁰C_m-r is maximum when:

5

10

15

20