Esercizi di Analisi 1

3.1)

a) (1 + x²)² - (1 + x)²(1 - x)²[ (1 + x)² + (2 - 1) ² ] =

= (1 + x)²(2 - x²) + 1 - (1 + x)² = 0

b)= 9x² + x₃ - 11 + x³ + 10

5.2)

= ∑₀⁵ 2 - 3∑₂⁵ = {∑₀⁷ - 4∑₂⁵ } = {2/√3}

ESERCIZIA 10 N:

∑_k=1^N (2k-1) = 4 + 3(1... + (1)n. n)...

= (M/7) ∑_k=1 (k∑_k=1) + 2∑_k=1 (k) - (N)

∑(A₀ +B₁) = ∑ Δ_A + ∑ Δ_B

∑a₀A = ∑_AA

x_k = q^k

1 ∑_k=0 (x -q)ⁿ = q^k[x⁴ + q₃ + x^n-1 x₂ qⁿ(x-q)(1-x) ] =

= (1 + q)q^q5+...+x^k(q -q)q⁵...✓ q_n+1 =

= (1 - q ⁿ⁺¹)

= {1 ∑²_k=0 qⁿ⁺⁴...

See g=1 (N + 1)

∑_k=1^N 1/k = ∑_k=1^N (1/k) = ∑_k=1^N 1/(k(k+1)) = ( 1/k - 1/(k+1) ) = (1 - 1/2) + ( 1/2 - 1/3)... +... (1/2 - 1/k )...= ( 1/2 q/n+1 ) = { q/N -1}

(∝ t k) ∑_k=1^N (∝)^(h) = ∑_k=0 ^N k^k-h

(n/k) = n! / k!(n-k)!

In quanti modi posso:

Disporre n ogettini - t c

K: a+c gli altri: = b