Question

Can someone help me with this series: I will write it out.

Answer 1

\[\sum_{1}^{\infty} 12i-7\]

Answer 2

i am asked to find the 15th partial sum?

Answer 3

again?

Answer 4

ok forget convergence this is way too big

Answer 5

there is a more or less snap way to find the 15th partial sum, but i always forget it so lets just do this
\[\sum_1^{15}15i-7=12\sum_1^{15}i-7\sum_1^{15}1\]

Answer 6

okay

Answer 7

this is just the distributive law and commutative law of addition in action, so i hope that part is clear.

Answer 8

yes i understand those, but i still need help please

Answer 9

ok so
\[\sum_1^{15}1=15\] with no thought, just 15 ones

Answer 10

hmm

Answer 11

so last term is
\[-7\times 15=-105\]

Answer 12

oh it does require thought. lets think but not too hard ok?

Answer 13

alright

Answer 14

\[\sum_1^{15}1=1+1+1+1+...+1\] fifteen of them!

Answer 15

clear now yes?

Answer 16

um, not really, your are saying the 15th partial sum is 15

Answer 17

hold on

Answer 18

i am doing it slowly step by step

Answer 19

my choices are : 178, 2670, 1246, and 1335

Answer 20

we need to compute
\[12\sum_1^{15}i-7\sum_1^{15}1\]

Answer 21

i am starting with
\[\sum_1^{15}1\] and i say that it is 15

Answer 22

okay

Answer 23

because you are adding 15 one up, and you get 15 when you do it
then multiply by -7 and get -105

Answer 24

so now we have
\[12\sum_1^{15}i-7\sum_1^{15}1=12\sum_1^{15}i-105\]

Answer 25

next we compute
\[\sum_1^{15}i\] and the formula for
\[\sum_1^{n}i=\frac{n(n+1)}{2}\]

Answer 26

in our case we get
\[\sum_1^{15}=\frac{15\times 16}{2}=120\]

Answer 27

no that is wrong
it is
\[12\times 120-105\]

Answer 28

1335, thanks sat

Answer 29

that is what i got. is it a choice i hope?

Answer 30

oh yeah i see it. ok
yw