Question

4. Express the series below in summation notation for the specified number of terms.
a. 2 + 4 + 8 + 16

Answer 1

\[\sum_{n=1}^{4} 2(n-1)\]

Answer 2

@ganeshie8 would this equation be like this

Answer 3

close, but not right

Answer 4

plugin n = 1,
do u get first term ?

Answer 5

2(1-1)

2(0)

0

NOPE

Answer 6

check again

Answer 7

2

Answer 8

\[\sum_{n=2}^{4} 2(n-1)\]

Answer 9

not exactly,
n = 2 to 4 is just three terms, but u have four terms in ur given series right ?

Answer 10

wait a sec,
the given sequence is GEOMETRIC, right ?

Answer 11

yes

Answer 12

find out the \(n^{th}\) term of series first

Answer 13

2 + 4 + 8 + 16

first term, \(a = 2\)
common ratio, \(r = 2\)

so, the \(n^{th}\) term is ?

Answer 14

2

Answer 15

dont remember the \(n^{th}\) term for geometric series ?

Answer 16

\(\large a_n = ar^{n-1}\)

Answer 17

plugin the values

Answer 18

2(2)^n-1

Answer 19

yes, so the sum notation can be written as :

\(\large \sum \limits_{n=1}^4 2(2)^{n-1}\)

Answer 20

simplifying gives u :

\(\large \sum \limits_{n=1}^4 2^{n}\)

Answer 21

could we write the equation either way

Answer 22

either way is fine