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Magazine Problem 35
Express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. $$1+2+3+\dots+30$$
Problem 35
Use the formula for the sum of the first n terms of a geometric sequence to solve. Find the sum of the first 11 terms of the geometric sequence: \(3,-6,12,-24, \dots\)
Problem 36
Write a formula for the general term (the nth term of each arithmetic sequence. Then use the formula for \(a_{n}\) to find \(a_{20}\), the 20th term of the sequence Find the sum of the first 25 terms of the arithmetic sequence: \(7,19,31,43, \dots\)
Problem 36
Express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. $$1+2+3+\cdots+40$$
Problem 36
Write the first three terms in each binomial expansion, expressing the result in simplified form. $$\left(x^{2}+1\right)^{17}$$
Problem 36
Use the formula for the sum of the first n terms of a geometric sequence to solve. Find the sum of the first 11 terms of the geometric sequence: \(4,-12,36,-108, \dots\)
Problem 37
Write a formula for the general term (the nth term of each arithmetic sequence. Then use the formula for \(a_{n}\) to find \(a_{20}\), the 20th term of the sequence Find the sum of the first 50 terms of the arithmetic sequence: \(-10,-6,-2,2, \dots\)
Problem 37
Use the formula for the sum of the first n terms of a geometric sequence to solve. Find the sum of the first 14 terms of the geometric sequence: \(-\frac{3}{2}, 3,-6,12, \ldots\)
Problem 37
Write the first three terms in each binomial expansion, expressing the result in simplified form. $$\left(y^{3}-1\right)^{20}$$
Problem 37
Express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. $$\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\dots+\frac{14}{14+1}$$
