Sequences and Series Flashcards
1
Q
How do you prove the formula for Sₙ of an arithmetic series?
A
Write Sₙ as the sum of each term (a, a+d, a+2d) ending with the last terms (l-d, l). Then write this equation in reverse and add each term together.
2
Q
What is the equation for nth term of a geometric series?
A
arⁿ⁻¹
3
Q
What is a convergent geometric series and when does it happen?
A
A sequence that has terms that decrease in size as n increases, only happens when -1 < r < 1 (or |r| < 1)
4
Q
How do you prove the formula for Sₙ of a geometric series?
A
Write Sₙ as the sum of each term (a, ar, ar²) ending with the last terms (arⁿ⁻², arⁿ⁻¹). Then write the equation again but multiplied by r. Subtract this equation from the first equation and all middle terms will cancel. Rearrange for the final equation.
