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Theory

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Procedure

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Posttest

References

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Binomial coefficients and Pascal's triangle

Choose difficulty:

Beginner

Intermediate

Advanced

For what value of

k

is the binomial coefficient of

a^{k}b^{5-k}

in the expansion of

(a+b)^5

equals

10

2

Explanation

3

Explanation

c: both

a

and

b

Explanation

d: none of the above Explanation

Explanation

Which of these constructions define Pascal's triangle?

a: binomial expansion of

(a+b)^c

where

c

is a constant and

a

b<=i

where

i

is the row number Explanation

Explanation

b: binomial coefficient

^{n}C_{r}

where

n

is the row number and

r

is the column number both starting at

0

Explanation

c: binomial expansion of

c^i

where

c

is a constant and

i

is the row number Explanation

Explanation

d: none of the above Explanation

Explanation

What does the summation of a row of Pascal's triangle represent?

a: binomial expansion of

(a+b)^n

for

a=b=1

where

n

is the number of elements in the row Explanation

Explanation

b: binomial expansion of

(a+b)^n

for

a=b=1

where

n

is the row index starting from

0

at the top of the triangle Explanation

Explanation

c: square of the summation of elements of the previous row Explanation

Explanation

d: none of the above Explanation

Explanation

If we add the values of second column third row in pascal's triangle for

(a+b)^n

and

(b+c)^n

, we get ______

ab+bc

Explanation

2(ab+bc)

Explanation

4

Explanation

d: none of these Explanation

Explanation

How can an element of Pascal's triangle be derived using existing elements?

a: by adding all the elements in the previous row and multiplying by the row index Explanation

Explanation

b: by adding the two elements directly on top of it in the previous row Explanation

Explanation

c: by adding all the elements in the previous row and multiplying by

2

Explanation

d: none of the above Explanation

Explanation

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