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C2 geometric series Ex 7F question 8

A sequence of numbers, u1,u2,u3....un,..... is given by the formula un= 3(2/3)^n -1 where n is a positive integer.
a) Find u1, u2 and u3
b) show that the sum of 15 un= -9.014 where n=1
c) prove that u = 2(2/3)^n -1
n+1
please help with parts two and three!! i cant prove or show.... much appreciated :rolleyes:
Reply 1
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joostan
13
Original post by gingeninge
A sequence of numbers, u1,u2,u3....un,..... is given by the formula un= 3(2/3)^n -1 where n is a positive integer.
a) Find u1, u2 and u3
b) show that the sum of 15 un= -9.014 where n=1
c) prove that u = 2(2/3)^n -1
n+1
please help with parts two and three!! i cant prove or show.... much appreciated :rolleyes:


Is that  un=3(23)n−1\ u_n = 3(\frac{2}{3})^{n-1} or
Unparseable latex formula:

\3(\frac{2}{3})^n - 1

?
Reply 2
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gingeninge
OP
Original post by joostan
Unparseable latex formula:

\3(\frac{2}{3})^n - 1

?


the latter of the two
Reply 3
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joostan
13
Original post by gingeninge
the latter of the two


How good is your sigma manipulation? :smile:
The original is the same as:
Sn= 3∑r=1n(23)n−∑r=1n1 S_n = \ 3 \displaystyle\sum_{r=1}^n (\frac{2}{3})^n - \displaystyle\sum_{r=1}^n 1
(edited 11 years ago)
Reply 4
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gingeninge
OP
OMG how did i miss that! thank you so much :-) :-)
Reply 5
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joostan
13
Original post by gingeninge
OMG how did i miss that! thank you so much :-) :-)


NP :tongue:

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