yht:
n=1
1
3 = 1
2
1=1
n=k
1
3+2
3+...+k
3 = (1+2+...+k)
2
n=k+1
1
3 + 2
3 + ... + k
3 + (k+1)
3 = (1+2+...+k+k+1)
2
(1+2+...+k)
2 + (k+1)
3 = (1+2+...+k+k+1)
2
(k+1)
3 = (1+2+...+k+k+1)
2 − (1+2+...+k)
2
1+2+...+k = t
(k+1)
3 = (t+k+1)
2 − t
2
(k+1)
3 = (t+k+1−t)(t+k+1+t)
(k+1)
3 = (k+1)(2t+k+1) |:(k+1)
(k+1)
2 = 2t+k+1
(k+1)
2 −(k+1) = 2t
k+1 = u
u
2 − u = 2t
u(u−1) = 2t
(k+1)(k+1−1) = 2t
(k+1)k = 2t
k(k+1) = 2*(1+2+...+k)
| | 1+k | |
1+2+...+k = |
| *k (suma k początkowych wyrazów ciągu arytmetycznego w którym a1=1, |
| | 2 | |
a
k=k)
k(k+1) = (1+k)*k
L = P
