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

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): You can put this solution on YOUR website!

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

RELATED QUESTIONS
In the expansion of (1+x)^21,the coefficient of (2r+1)th term is equal to the coefficient (answered by KMST)

Hai Sir, please help me on this problem, i could find the soultion If (m+1)th term of... (answered by stanbon)

find the nth term of an A.P. whose (r+1)th term is... (answered by stanbon)

The demension of a rectangular prism are 2 m, 6 m, and x m, it's volume is 193 m cubed... (answered by ikleyn)

find the first term of the AP, if the 2pth term is 50 more than the pth term, and the... (answered by ikleyn)

If 21st and 22nd term of the expansion (1+x)^44 are equal find the value of x (answered by greenestamps)

The Fibonacci sequence is obtained as follows: The first number is 1, the second number... (answered by Edwin McCravy)

The nth term of a series is 1/2(2n-1). Write down the (n+1)th... (answered by ikleyn)

The sum to m term of the series 1 +11+111...... upto m term is equal... (answered by math_helper)