hi! can you help me with this question? (1 Viewer)

[icyeyes]

hey!
i'm having trouble with this question- i just cant get the answer!

Find the number of terms needed to be added for the sum to exceed 1000 000 in the series 4+16+64....

thanx so much 4 your time!

 

[Xayma]

S_n=a(rⁿ-1)/(r-1)

Now S_n>1 000 000

a(rⁿ-1)/(r-1)>1 000 000
4(4ⁿ-1)/(3)>1 000 000
4(4ⁿ-1)>3 000 000
4ⁿ⁺¹-4>3 000 000
4ⁿ⁺¹>3 000 004
ln 4ⁿ⁺¹>ln 3 000 004
(n+1) ln 4 > ln 3 000 004
n+1> (ln 3 000 004)/(ln 4)
n > (ln 3 000 004)/(ln 4) -1

n>9.758266
ie 10 terms are needed.

 

[icyeyes]

thanx!

thanx for that!

 

[jarro_2783]

where did you learn a(r^n-1)/(r-1), if you use ar^(n-1) it makes it a whole lot easier.

How do you do superscripts on this forum?

 

[Archman]

where did you learn a(r^n-1)/(r-1), if you use ar^(n-1) it makes it a whole lot easier.

hmm wat the?

 

[Numero Uno]

ehh ar^(n-1)
is the specific term in the geometric series

Sn=a(rn-1)/(r-1) is the sum of the geometric series where r>1

hmmm i dunno what ur on about ...

 

[Xayma]

where did you learn a(r^n-1)/(r-1), if you use ar^(n-1) it makes it a whole lot easier.

How do you do superscripts on this forum?

ar^n-1 is for an individual term.

We are looking for the sum of the terms.

Which is given by S_n=a(rⁿ-1)/(r-1)

 

[Estel]

And thus dies an attempt at sabotage