MATHEMATICAL INDUCTION AND RECURRENC Solve the following. (10 pts each) 1. Prove P(n) = n2 (n + 1) 2. Recurrence relation an = 2n with the initial term a1 = 2.
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Here's the Solution to this Question
1. Given statement is-
at , Which is even
P(1) is true.
Let us assume that P(k) is true for some positive integer k,
Now put
As is even so,
P(k+1) is true
Hence Given statements is true for all .
2.
at
at
at
The Required sequence is-
The required recurrence relation is
Where and 1. Given statement is-
at , Which is even
P(1) is true.
Let us assume that P(k) is true for some positive integer k,
Now put
As is even so,
P(k+1) is true
Hence Given statements is true for all .
2.
at
at
at
The Required sequence is-
The required recurrence relation is
Where and 1. Given statement is-
at , Which is even
P(1) is true.
Let us assume that P(k) is true for some positive integer k,
Now put
As is even so,
P(k+1) is true
Hence Given statements is true for all .
2.
at
at
at
The Required sequence is-
The required recurrence relation is
Where and