9. Sequences, Series, & Induction

The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a₁=3 and a_n=4a_n-1 for n≥2

The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a₁=4 and a_n=2a_n-1 + 3 for n≥2

In Exercises 19–22, the general term of a sequence is given and involves a factorial. Write the first four terms of each sequence. a_n = n²/n!

In Exercises 19–22, the general term of a sequence is given and involves a factorial. Write the first four terms of each sequence. a_n=2(n+1)!

Evaluate each factorial expression. 17!/15!

Evaluate each factorial expression. 16!/2!14!

Evaluate each factorial expression. (n+2)!/n!

Find each indicated sum. ${\sum }_{i=1}^{6}5i$

Find each indicated sum. ${\sum }_{i=1}^{4}2i^2$

Find each indicated sum. ${\sum }_{k=1}^{5}k(k+4)$

Find each indicated sum. ${\sum }_{i=1}^4{(-\frac{1}{2})}^i$

Find each indicated sum. ${\sum }_{i=5}^{9}11$

Find each indicated sum. ${\sum }_{i=0}^4\frac{(-1{)}^i}{i!}$

Find each indicated sum. ${\sum }_{i=1}^5\frac{i!}{(i-1)!}$

Express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. $1^2+2^2+3^2+\cdots +{15}^2$