SOLUTION: If the coefficients of (m+1)th term and the (m+3)th term in the expansion of (1+x)^20 are equal then the value of m is-:
a)10
b)9
c)8
d)7
Algebra ->
Permutations
-> SOLUTION: If the coefficients of (m+1)th term and the (m+3)th term in the expansion of (1+x)^20 are equal then the value of m is-:
a)10
b)9
c)8
d)7
Log On
Question 1088714: If the coefficients of (m+1)th term and the (m+3)th term in the expansion of (1+x)^20 are equal then the value of m is-:
a)10
b)9
c)8
d)7 Answer by Edwin McCravy(20055) (Show Source):
20C(m+1) = 20C(m+3)
If we knew enough about the symmetry of Pascal's triangle we'd
know that the middle term would have coefficient 20C10 and therefore
10 would have to be halfway between m+1 and m+3, so 10 would be
their average
However, we'll do it assuming we didn't know that much about Pascal's
triangle. We use the definition of combinations:
Numerators are equal so denominators must also be equal:
Divide both sides by (m+1)!
Divide both sides by (17-m)!
"FOIL" out both sides:
Edwin
