Difference between revisions of "2005 iTest Problems/Problem 7"
(Created page with "==Problem== Find the coefficient of the fourth term of the expansion of <math>(x+y)^{15}</math>. ==Solution 1== The coefficient of the <math>n</math>th term in the expansion...") |
(→Solution 1) |
||
| Line 4: | Line 4: | ||
==Solution 1== | ==Solution 1== | ||
The coefficient of the <math>n</math>th term in the expansion of <math>(x+y)^m</math> is <math>\binom{m}{n}</math>. Plugging in <math>15</math> for m and <math>4</math> for n, we find that our answer is <math>\binom{15}{4}=\boxed{1365}</math>. | The coefficient of the <math>n</math>th term in the expansion of <math>(x+y)^m</math> is <math>\binom{m}{n}</math>. Plugging in <math>15</math> for m and <math>4</math> for n, we find that our answer is <math>\binom{15}{4}=\boxed{1365}</math>. | ||
| + | |||
| + | ==See Also== | ||
| + | {{iTest box|year=2005|num-b=6|num-a=8}} | ||
Revision as of 16:56, 13 October 2025
Problem
Find the coefficient of the fourth term of the expansion of 
.
Solution 1
The coefficient of the 
th term in the expansion of 
is 
. Plugging in 
for m and 
for n, we find that our answer is 
.
See Also
| 2005 iTest (Problems, Answer Key) | ||
| Preceded by: Problem 6 |
Followed by: Problem 8 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 • 51 • 52 • 53 • 54 • 55 • 56 • 57 • 58 • 59 • 60 • TB1 • TB2 • TB3 • TB4 | ||
