currysauce
Actuary in the making
Find the sum of the first 10 terms of the series
3+7+13+...+[2^n +(2n-1)] +...
3+7+13+...+[2^n +(2n-1)] +...
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Need help on a series queston (1 Viewer)
- Thread starter currysauce
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jm1234567890
Premium Member
split it up
geometric + arithmetic -1
sum = (2n+1 -1)/(2-1) + 2*(n/2)(n+1) - n
when n = 10
sum = 2049 + 110 - 10 = 2149
geometric + arithmetic -1
sum = (2n+1 -1)/(2-1) + 2*(n/2)(n+1) - n
when n = 10
sum = 2049 + 110 - 10 = 2149
Last edited:
currysauce
Actuary in the making
jm could u explain it please....
jm1234567890
Premium Member
do you understand how to derrive the formulas for geometric and arithmetic series?currysauce said:
currysauce
Actuary in the making
yes, but not how u have done it
Trev
stix
Find the sum of the first 10 terms of the series
3+7+13+...+[2^n +(2n-1)] +...
This is the same as:
When n = 1; = 2 + 1
when n = 2; = 4 + 4
when n = 3; = 8 + 5
Therefore, you have a geometric and arithmetic series as such:
2 + 4 + 8 + ... 2<sup>10</sup> (geometric)
plus
1 + 4 + 5 + ... (2.10 - 1) (arithmetic)
Now use your formula's.
3+7+13+...+[2^n +(2n-1)] +...
This is the same as:
When n = 1; = 2 + 1
when n = 2; = 4 + 4
when n = 3; = 8 + 5
Therefore, you have a geometric and arithmetic series as such:
2 + 4 + 8 + ... 2<sup>10</sup> (geometric)
plus
1 + 4 + 5 + ... (2.10 - 1) (arithmetic)
Now use your formula's.