Question

exercițiile sunt in poza doar ex 20 urgent !!!!!!!!​

Answer 1

Răspuns:

Generalizam tipul de suma intalnita in exercitiul 20.

S = 1/1*2 + 1/2*3 + 1/3*4 + ... + 1/(n-1)(n)

1/ab =(b - a)/ab = b/ab - a/ab =

= 1/a - 1/b

Unde b = a+1.

S = 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 ...... + 1/(n-1) - 1/n

S = 1 - 1/n = n/n - 1/n = (n-1)/n

20.

a) rad[102/99 * (50/ 51 - 101/102 + 50/51)] =

= rad[102/99 * (200/202 - 101/102)] =

= rad(102/99 * 99/102) =

= rad(1) = 1

b) rad[128*126*(63/64 - 62/63)] =

= rad[128*126*(63*63 - 62*64)/63*64] =

= rad[4*(63^2 - (63-1)(63+1))] =

= 2rad(63^2 - 63^2 + 1) =

= 2rad(1) =

= 2

c) rad[120/29 * (44/45 - 89/90 + 44/45)] =

= rad[120/29 * (88/45 - 89/90)] =

= rad[120/29 * (176 - 89)/90] =

= rad(120/29 * 87/90) =

= rad(36/9) =

= rad(4) =

= 2.