Sigma Notation
Sigma notation, often denoted by the symbol Σ, is a concise mathematical representation used to express the sum of a sequence of terms. Widely employed in various branches of mathematics, this notation provides a convenient way to articulate repetitive additions. It succinctly captures the essence of summation, allowing mathematicians to express complex series with clarity and brevity. By encapsulating the cumulative nature of mathematical operations, sigma notation enhances the efficiency of conveying mathematical concepts and facilitates concise communication in the realm of equations and series.
Questions
- How do you use the summation formulas to rewrite the expression #Sigma (2i+1)/n^2# as i=1 to n without the summation notation and then use the result to find the sum for n=10, 100, 1000, and 10000?
- How do you use the properties of summation to evaluate the sum of #Sigma (i-1)^2# from i=1 to 20?
- How do you use sigma notation to write the sum for #1-1/2+1/4-1/8+...-1/128#?
- What is the integral of #sqrt(sinx)cosx dx#?
- How do you use summation notation to expression the sum #7+14+28+...+896#?
- How do you find the sum of the finite geometric sequence of #Sigma 5(3/5)^n# from n=0 to 40?
- How do you find a formula for the sum n terms #Sigma (1+(2i)/n)^3(2/n)# and then find the limit as #n->oo#?
- How do you find the sum of #Sigma 2i^2# where i is [0,5]?
- How do you find the partial sum of #Sigma (250-8/3i)# from i=1 to 60?
- How do you evaluate the sum represented by #sum_(n=1)^5n/(2n+1)# ?
- How do you find the sum given #Sigma 1/j# from j=3 to 5?
- If #sum_(n=2) ^oo (1+k)^-n=2# what is #k#?
- How do you find the partial sum of #Sigma (2n-1)# from n=1 to 400?
- How do you use sigma notation to write the sum for #[1-(1/6)^2]+[1-(2/6)^2]+...+[1-(6/6)^2]#?
- How do you find the sum of the finite geometric sequence of #Sigma 8(-1/2)^i# from i=0 to 25?
- How do you find the sum of the finite geometric sequence of #Sigma 2(4/3)^n# from n=0 to 15?
- How do you use the summation formulas to rewrite the expression #Sigma (4j+3)/n^2# as j=1 to n without the summation notation and then use the result to find the sum for n=10, 100, 1000, and 10000?
- What is the value of #log_2(Pi_(m=1)^2017Pi_(n=1)^2017(1+e^((2 pi i n m)/2017)))# ?
- How do you evaluate the series #Sigma 5r# from r=3 to 8?
- How do you find a formula for the sum n terms #sum_(i=1)^n (16i)/n^3# and then find the limit as #n->oo#?