Zadanie 1f
For un = (2n + 1)3 − (2n − 1)3, (i) suggest an expression for ; (ii) prove it using the definition of u.
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For un = (2n + 1)3 − (2n − 1)3, (i) suggest an expression for ; (ii) prove it using the definition of u.
The two bounds to verify are and . Again un = (2n + 1)3 − (2n − 1)3. (i) Express u_n as a quadratic in v = 2n + 1. (ii) Hence express in terms of T2(n), T1(n), T0(n). (iii) Hence show that…
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Initially w=3, p=1/3 and charge is 1. (i) Show that the probability a of still running with charge 1 after exactly two ticks is 2/9. (ii) Find the probability b that full charge is reached for the first time on tick 4.
Under the same w=3, p=1/3 settings, a run is still active at charge 1 after tick 4. State the probability that it is again active at charge 1 after the next two ticks.