PEQUOD

Quantum/Theoretical/Computational Chemistry Professor George Maroulis

Department of Chemistry University of Patras GR-26500 Patras Greece

Patras, Tuesday, October 18, 2016 Να υπολογισθουν τα αθροισματα 1.

∑ 500 𝑛=1 1 𝑛 2𝑛 2. ∑ 500 𝑛=1 1 2n+1 3.Να υπολογισθει το αθροισμα 1 4 + 2 4 + 3 4 + ... + 100 4 και να επαληθευθει το αποτελεσμα δεδομενου οτι [1,06389] [3,09006] [2.050.333.330] 100 

n

 1

n

4   1)(2

n

 1)(3

n

2  3

n

 1) / 30 4.. Να υπολογισθει η τιμη του π με ακριβεια πεντε δεκαδικων ψηφιων. Διδεται  ∑ ∞ 𝑛=1 1 𝑛 2 = 𝜋 2 6 [3,14159] Π=4*ΑΤΝ(1) Merciles Beaute Your yen two wol slee me sodenly; I may the beautee of hem not sustene, So woundeth hit thourghout my herte kene. And but your word wol helen hastily My hertes wounde, while that hit is grene, Your yen two wol slee me sodenly; I may the beautee of hem not sustene. Upon my trouthe I sey you feithfully That ye ben of my lyf and deeth the quene; For with my deeth the trouthe shal be sene. Your yen two wol slee me sodenly; I may the beautee of hem not sustene, So woundeth it thourghout my herte kene. Geoffrey Chaucer(?)