Question

Find the sum of the series 5+55+555+... to n terms, let f(n) be Sn, then verify that S2=60 when n=2 using f(n), and lastly, establish that 81/x f(n) is always a multiple of 81

Answer 1

Do you know the equation for the nth term? You're right, these are pretty hard.

Answer 2

a = 5
tn=a(n-1)+5*10^(n-1)

Does this seem right?

Answer 3

ahhhmmm, I've worked on it for so long, but there seems to be no progress

Answer 4

I dont know....

Answer 5

first term is 5*1
2nd= 5*12
3rd=5*123
4th=5*1234

Do you see the rule?

Answer 6

still I do not see how to change this into direct equation

Answer 7

yeah, maths HL in the IB diploma is unbelievably hard

Answer 8

what is HL and IB?

Answer 9

I am thinking of writing it up as a sum

Answer 10

\[5*\sum_{1}^{n} n10^{n-1}\]

Answer 11

Do you think it is right? :-)

Answer 12

I will post it again so someone can check it, ok?

Answer 13

HL is for higher level and IB is for International Bacchalerette

Answer 14

thanx

Answer 15

the answer is 5/81(10^(n+1)−9n−10)

Answer 16

check my topic if you need the calculation

Answer 17

thank you so much! but what do you mean by check my topics?

Answer 18

I reposted ur question

Answer 19

loved this problem btw! So thanks for posting

Answer 20

no, thank YOU for helping me with this! my maths teacher gaved these questions to me and told me that it took her a long time to do them too :-/