My Math Forum Binomial theorem

 Probability and Statistics Basic Probability and Statistics Math Forum

 April 16th, 2012, 08:05 AM #1 Senior Member   Joined: Apr 2012 Posts: 112 Thanks: 0 Binomial theorem Hello! I have questions on the binomial theorem. I thought they looked alright and attempted them, only to find that I could not solve them, or my answers are wrong... 1.) Find the value of n if the coefficient of x^3 in the expansion of (2+3x)^n is twice the coefficient of x^2. 2.) In the binomial expansion of (1+(1/3))^n in ascending powers of 1/3, the fourth and fifth terms are equal. Find the value of n.
 April 16th, 2012, 08:34 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Binomial theorem 1.) We may state: ${n \choose 3}2^{n-3}3^3=2{n \choose n}2^{n-2}3^2$ $3{n \choose 3}=4{n \choose 2}$ $\frac{1}{2}n(n-1)(n-2)=2n(n-1)$ $\frac{1}{2}(n-2)=2$ $n-2=4$ $n=6$ 2.) We may state: ${n \choose 3}$$\frac{1}{3}$$^3={n \choose 4}$$\frac{1}{3}$$^4$ ${n \choose 3}=\frac{1}{3}{n \choose 4}$ $\frac{n(n-1)(n-2)}{6}=\frac{n(n-1)(n-2)(n-3)}{72}$ $12=n-3$ $n=15$

 Tags binomial, theorem

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post muhsentdrawjiac Probability and Statistics 1 June 14th, 2012 12:44 PM Keroro Probability and Statistics 4 June 12th, 2012 03:43 AM Keroro Probability and Statistics 6 June 10th, 2012 11:59 AM mcshine Probability and Statistics 3 May 4th, 2012 12:45 PM coolhandluke Applied Math 4 March 25th, 2010 04:21 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top