SOLUTION: Express the given sums using sigma notation for the following: a) 2+5+10+14+18 b) 5+25+125+625 c) 1/2+1/2×3+1/3×4+...+1/99×100 Thank you in advance for your help.

Algebra ->  Sequences-and-series -> SOLUTION: Express the given sums using sigma notation for the following: a) 2+5+10+14+18 b) 5+25+125+625 c) 1/2+1/2×3+1/3×4+...+1/99×100 Thank you in advance for your help.      Log On


   

Question 887613: Express the given sums using sigma notation for the following:
a) 2+5+10+14+18
b) 5+25+125+625
c) 1/2+1/2×3+1/3×4+...+1/99×100
Thank you in advance for your help.
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Express the given sums using sigma notation for the following:
a) 2+6+10+14+18:::: SUM[2+(n-1)4] from n = 1 to n = 4
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b) 5+25+125+625:::: SUM[5^n] from n = 1 to n = 4
----------------------------------------------------
c) 1/2+1/2×3+1/3×4+...+1/99×100:::
SUM[(1/2) + (1/n)*(n+1)] from n = 1 to n = 99
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Cheers,
Stan H.
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Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
a) 2+5+10+14+18

We can't put that in sigma notation because there is no obvious pattern
to those numbers as there is for (b) and (c).  Are you sure you copied (a)
right?

I see that the other tutor assumed you meant 6 instead of 5.  Then it's 

2+6+10+14+18 = 4-2,8-2,12-2,16-2,20-4.  Each term is 2 less than a multiple
of 4 or 4k-2 

sum%28%284k-2%29%2Ck=1%2Cmatrix%281%2C2%2C%22%22%2C5%29%29

b) 5+25+125+625.  That's 5%5E1%2B5%5E2%2B5%5E3%2B5%5E4.  Each term is of the form 5%5Ek where k goes from 1 to 4 




c) 1/2+1/2×3+1/3×4+...+1/99×100

That's .  Each term
is of the form 1%2F%28k%2A%28k%2B1%29%29 where k goes from 1 to 99.



Edwin