1. Which row of Pascal’s triangle has terms that sum to 648?
2. Find the fourth term of the expansion of (2? − 1) .
2) The expansion of 2x-1 has only two terms. Therefore we can't find the fourth term in expansion. Please check if there is any power for (2x-1). Please comment if any changes. I will give you answer.
1. Which row of Pascal’s triangle has terms that sum to 648? 2. Find the fourth...
Pascal’s triangle gives a method for calculating the binomial coefficients. It begins as follows: (picture #1)The (n+ 1)th row of this table gives the coefficients for (a+b)^n = ∑^nr=0 nCk arbn-rThe next row is found by adding the two numbers above the new entry, i.e.(picture #2)Prove this equation using the mathematical definition of a combination.!!!!!!
Help with Pascal’s Triangle: Paths and Binary Strings Suppose you want to create a path between each number on Pascal's Triangle. For this exercise, suppose the only moves allowed are to go down one row either to the left or to the right. We will code the path by using bit strings. In particular, a O will be used for each move downward to the left, and a 1 for each move downward to the right. So, for example, consider...
a. Find the sum of the series to 'n-l'terms 2 1+Vx + 2 2 1- x' 1-7X + + ... to 'n-l' terms b. If the fifth term of the sequences is 10 and fifteenth term is 30, find the arithmetic sequences.
im lost 21. Which of the following fourth-row elements could be "x" in the below ion? a. Ge b) As Se d) Kr e ) none of these 2- o=*:
Find the sum of the first 28 terms of a geometric sequence whose third term is a3 = 6 and whose eighth term is a8 = 15.62.
write this python program 4. Pascal Triangle. Write a program pascal.py that builds and prints a two-dimensional list (a list of lists) a such that a[n][k contains the coefficient of the k-th term in the binomial expansion of (ty) These coefficients can be organized in a triangle, famously known as Pascals triangle. Every row in the triangle may be computed from the previous row by adding adjacent pairs of values together. Below is a sample invocation of the program s...
Prove: If n=2^(k)−1 for k∈N, then every entry in row n of pascal's triangle is odd.
Find a formula for the sum of n terms. Use the formula to find the limit as n →0. n lim n00 -(i – 1)2 i = 1 Free
[i 1 -2] (a) Find det 2 3 5 by expansion along the 2nd row. (1 -1 3 (b) Use Cramer's rule to find the value of x in the solution to the system of linear equations shown below. (You may want to use your answer in part (a)). +y-2x = 0 2x + 3y + 5z = 3 2-y+32 = 0
7) Write the terms and find the sum of the finite series 2" (4 pts)