Need help with summations.?

Question

The instructions are: use the summation formulas to rewrite the expression without the summation notation. Use the result to find the sum for n=10, 100, 1000, and 10000:
n summation quotation then
i = 1

the problem is :2i + 1/n^2

Answer 1

OK. Since all of the terms have a constant term of 1/n² you can factor that out to get
(1/n²) * (2i+1) for i = 1 to 10 etc.
Now, the sum of the first n odd numbers is known to be n² (1+3 = 4 = 2², 1+3+5 = 9 = 3² and so on) so the sum as i goes from 1 to whatever will be
3+5+7+9+...... and the sum of that will be n²-1 (since the 1 didn't show up) and the final expression is
(n²-1)/n²

HTH

Doug

Answer 2

that is easy, i think, if i got u right.. u said i is going from 1 to n, right? so than it is only that 2i changes.

so for n=10 it is from 1 to 10, so it is 10*1/n^2 plus (2 + 2*2 + 2*3 +...+2*10) and that is 1/10 + 2*(1+2+...+n) = 1/10 + 2*(1+9)

so the formula for all n would be:
1/n + n*(n-1)

not so sure, im on the spring vacation now :) and i think this is the problem for a child from a 9th grade..

Answer 3

1