Pascal's Triangle
What is the 4th row of the triangle? (Starts with the 0th row)
1, 4, 6, 4, 1
Expand (2x-y)5
32x5 - 320x4y + 80x3y2 - 40x2y3 + 10xy4 - y5
Find the coefficient of x3 in (x+7)4.
28
What is 10 choose 3?
120
Which famous person invented the binomial theorem? (hint hint...we've heard his name a lot this year)
Isaac Newton
What is the sum of the elements in the 10th row of Pascal's Triangle?
1024
Find the coefficient of x5 in the expansion of (x+3)12.
173204
Expand and simplify (x - (2/x))^4.
x4-8x2+24-(32/x2)+(16/x4)
What is 1 choose 2?
0
Where is Pascal from?
France
What kind of numbers make up the third diagonal of the triangle?
Triangle Numbers
Find the coefficient of x4y5 in the expansion of (3x-2y)9.
326592
What is the constant term of the expansion of (3x2 - (1/x))9?
2268
How many different 4 letter words (meaning just a string of letters) can be made from the letters of EFFERVESCENCE?
2401
What is Pascal's first name?
Prove why the kth element of the nth row of Pascal's Triangle is equal to 'n choose k.'
Judges will decide.
Find the coefficient of x5 in the expansion of (3x-2)8.
Find the coefficient of x-2 in the expansion of (x-1)3((1/x) + 2x)6.
What is 21 choose 5?
20349
What is Pascal's Wager?
"It is rational to believe in God because the potential rewards of believing are far greater than the potential losses of not believing."
What is Pascal's Identity?
(n choose k) = (n-1 choose k-1) + (n-1 choose k)
Find the constant term in (x2-(2/x))9.
5376
Consider the expansion of x2(3x2 + (k/x))8. The constant term is 16,128. Find k.
k=+/- 2.
How many 0's are at the end of the number 100 factorial?
24
When was Pascal born? (closest answer wins)