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i need help asap. follow instructions. i have attached the instructions. ASAP

i need help asap. follow instructions. i have attached the instructions. ASAP i need help asap. follow instructions. i have attached the instructions. ASAPi need help asap. follow instructions. i have attached the instructions. ASAP

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Innite Series with Maple Name Open a new Maple worksheet and put your name at the top. Work through these instructions, then the exercises at the end. Maple’s sum command can be used to evaluate both finite and infinite sums. 50 X For instance, 3n may be entered as: n=1 sum(3*n, n=1 .. 50); Maple can even find a formula for some indefinite sums. n X Noe you try: Use the sum command to evaluate: i i =1 Have Maple simplify the result by immediately executing simplify(%); This is Gauss’s formula for the sum of the first n integers, 1 + 2 + · · · + n = P Maple can find similar formulas for ni=1 i p for several small values of p. n(n + 1) . 2 sum(i^2, i=1 .. n) sum(i^5, i=1 .. n) sum(i^(-1), i=1 .. n) Notice the last example does not give a compact formula. Maple can work with infinite series as well. Simply insert the word infinity as the upper bound in the sum command. For instance, sum( (1/2)^n, n=1 .. infinity ); If we try this with a divergent series we see that Maple simply prints the infinity symbol. Try to have Maple evaluate a divergent series of your choice. Now let’s try another convergent series. sum(1/n^3, n=1 .. infinity); Maple returns the value of this series using its Zeta function. This is an internal function used in numerical approximations. To get an approximation of this sum execute: evalf(%); This command tells Maple to evaluate the previous result as a floating point, or decimal, result. 1 Exercises Open a new worksheet and answer the following questions. Be sure to add text comments explaining your work. You may discuss problems with each other, but be sure to do your own work! 1. Use Maple to evaluate ∞ X 1 k=1 k 2 + 3k + 2 then evaluate the sum by hand. Do you get the same answer? 2. Use Maple to evaluate the following geometric series. If it doesn’t immediately give a numeric answer be sure to use the evalf command. Confirm that Maple gives the expected values. ∞ µ −4 ¶n ∞ µ 4 ¶n X X n=1 3 n=1 5 ∞ ∞ ³ e ´n X X (−1)n 5 3 n=1 n=0 s 3. Use Maple to evaluate ∞ 6 X 2 n=1 n 2
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