Find the meall, 11
the other numbers.
11./There are four unknown numbers. The mean of the first two numbers is 4 and the
of the first three is 9. The mean of all four number is 15, if one of the four number
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Answer:
give me 5
Step-by-step explanation:
When we multiply this out we will have a sum of terms each of which results from
a choice of an a or b for each of n factors. When we choose j a’s and (n − j) b’s,
we obtain a term of the form aj bn−j . To determine such a term, we have to specify
j of the n terms in the product from which we choose the a. This can be done in
¡n
j
¢
ways. Thus, collecting these terms in the sum contributes a term ¡n
j
¢
aj bn−j . ✷
For example, we have
(a + b)
0 = 1
(a + b)
1 = a + b
(a + b)
2 = a2 + 2ab + b2
(a + b)
3 = a3 + 3a2b + 3ab2 + b3 .
We see here that the coefficients of successive powers do indeed yield Pascal’s tri-
angle
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