Find a formula for for sum of n terms.Use the formula to find limit as n approaches infinity.
sigma notation start i=1 end n
((1+(i/n))((2/n))
Would anyone kindly help me with this problem.
Find a formula for for sum of n terms.Use the formula to find limit as n approaches infinity.
sigma notation start i=1 end n
((1+(i/n))((2/n))
Would anyone kindly help me with this problem.
I guess you mean this:
$\displaystyle \sum_{i=1}^{n} \frac{1+\frac{i}{n}}{\frac{2}{n}}$
?
Write it as:
$\displaystyle \sum_{i=1}^{n} \frac{1+\frac{i}{n}}{\frac{2}{n}}=\sum_{i=1}^{n} \frac{\frac{n+i}{n}}{\frac{2}{n}}=\sum_{i=1}^{n} \frac{n+i}{2}$
Do you recognize a 'special' serie? ...
This is a Riemann sum for:
$\displaystyle I=\int_0^2 (1+x/2)\; dx$
If you have arrived at the limit from the Riemann sum you should say so, otherwise you will probably get the integral as the answer for the limit rather than the sum of the finite series followed by limiting.
CB