Let a0 = 1, a1 = 2, a2 = 3 and an = an-1 + an-2 + an-3 for n ≥ 3. Prove that an ≤ 3n for all positive integers n.
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Given:
Let a0 = 1, a1 = 2, a2 = 3 and an = an-1 + an-2 + an-3 for n ≥ 3.
To Prove:
Prove that an ≤ 3n for all positive integers n.
Solution:
it is given that a0 = 1, a1 = 2, a2 = 3
and we know that d = common difference is-
here,
also , we know that-
therefore, in R.H.S. is
for ,
from above, calculation
for all positive integers n.
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