Find the sum of n terms from the sequence (1,2,4,7,11,...,an)
Algebra
Level
3
Sn = 1+2+4+7+11+...+an
(n+1)n(2n+1)/6 + n(n+1)/2 + n
(n+1)n(2n+1)/12 + n(n+1)/4 + n
(n+1)n(2n+1)/12 + n(n+1)/4 + n/2
(n+1)n(2n+1)/6 + n(n+1)/2 + n/2
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1 solution
A n = A n-1 + n A n-1 = A n-2 + n - 1 ... A n = A n-2 + (n-1) + n A n = A n-3 + (n-2) + (n-1) + n ... A n = A n-k + (n-k+1) + ... + n
k = n
A n = A 0 + n(n+1)/2
A_0 = 1
A_n = 1 + n(n+1)/2
...
S_n = ∑ (n(n+1)/2 +1)
S_n = ∑(n²/2 + n/2 + 1)
S_n = (n+1)n(2n+1)/6 + n(n+1)/2 + n
S_n = (n+1)n(2n+1)/12 + n(n+1)/4 + n