tolong jawab yg no 2b & 2e

jawab

(2b)

1+2+4+8+...+2ⁿ⁻¹ = 2ⁿ - 1
n = 1 → 2⁰ = 2 -1 → 1  = 1 (benar)
n = k → 1 + 2 + 4+ 8 + ...+2^(k-1)  = 2^(k)  - 1
n =  k+1 → 2^(k) - 1  +2^(k+ 1-1)  = 2^(k+1)  - 1
2^(k)  - 1 + 2^(k)  = 2^(k+1) - 1
2. 2^k  - 1 = 2^(k+1)   -1
2^(k+1) - 1 = 2^(k+1) - 1

(2e)
1.2 + 2.3 + 3.4 + ...+n(n+1) = n(n+1)(n+2)/3
n = 1 → 1(1+1) = 1(1+1)(1+2)/3 →  2 = 2
n = k → 1.2 + 2.3 + 3.4 + ...+ k(k+1) = k(k+1)(k+2)/3
n = k+1 → k(k+1)(k+2)/3 + (k+1)(k+1+1) = (k+1)(k+1+1)(k+1+2)/3
k(k+1)(k+2)/3 +  (k+1)(k+2)  = (k+1)(k+2)(k+3) /3
{k(k+1)(k+2) + 3(k+1)(k+2)}/3 = (k+1)(k+2)(k+3) / 3
(k+1)(k+2)(k+3) / 3 = (k+1)(k+2)(k+3)/3