1)Find a formula for Sn, the sum of the first n terms of the series:
a) √3 + 3 + 3√3 + 9 +...
b) 12 + 6 + 3 + 3/2 +...
2) A geometric sequence has partial sums S1=3 and S2=4
a) state the first term U1
b) Calculate the common ratio r
c) Calculate the fifth term U5 of the series
PLEASE HELP !
1) a. Sum =F x (1 - r^n) / (1 - r), F=First term, r=common ratio, n=number of terms.
b.Sum of infinite series =F / (1 - r ), variables same as above.
2) a. Given partial sums, it follows that the first term =3
b. The common ratio is 1/3
c. The 5th term will be: 1/27
This is an infinite series which sums to 4.5.
+129839 1)Find a formula for Sn, the sum of the first n terms of the series:
a) √3 + 3 + 3√3 + 9 +...
b) 12 + 6 + 3 + 3/2 +...
2) A geometric sequence has partial sums S1=3 and S2=4
a) state the first term U1
b) Calculate the common ratio r
c) Calculate the fifth term U5 of the series
1 (a) Sn = √3 [ 1 - √3n ] / [ 1 - √3] note, this series will have an infinite sum
1 (b) Sn = 12/ [ 1 - 1/2n] / [ 1 - 1/2] = 24 [ 1 - 1/2n ] ....note that.....as n grows larger, the series sum converges to 24
2 (a) The first term = 3
2 (b) The common ratio is 1/3
2 (c) The 5th term is given by 3(1/3)^[5-1] = 3(1/3)^4 = 3/81 = 1/27
