Question
The sum of the coefficients in the expansion of the expression (a + b)n is 64. Use Pascal’s triangle to find the value of n.
Hint:
Pascal's Triangle is a method to know the binomial coefficients of terms of binomial expression (x + y)n , where n can be any positive integer and x,y are real numbers. Pascal Triangle is represented in a triangular form, it is kind of a number pattern in the form of a triangular arrangement. We are asked to find the values of n in ( )n a b when the sum of coefficient is 64, using the Pascal’s triangle.
The correct answer is: n=6.
Step 1 of 1:
The Pascal’s triangle is:
The value of n is 64, which is 26 . Then, find the value of 6+1=7th row. Thus, we have:
1 + 6 + 15 + 20 + 15 + 6 +1 = 64
Hence, the value of n=6.
The value of n is 64, which is 26 . Then, find the value of 6+1=7th row. Thus, we have:
To find the value of n when the sum of coefficients is given, we have to write them as the power of two. The power would be the value of n.
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Using Pascal's Triangle, where n can be any positive integer as x and y are real numbers, one can determine the binomial coefficients of the terms of the binomial formula (x + y)n. Pascal Triangle is a type of number pattern that appears as a triangular arrangement and is represented by triangles. It starts with '1' at the top and continues with '1' on the triangle's two sides. Each new number in the Pascal triangle has equal values to the sum of the two integers above and below. The probability conditions in which this triangle is utilized vary. Every row represents this table's coefficient of expansion of (x + y)n. Zero row n = 0, (x + y)0
