Find the value of i n- in-1-in-2-in-3 for all n - N-

i nbsp;^n+ i^n+1+i^n+2+i^n+3 = i^n [1 + i + i^2 +i^3]= i^n [1 + i 1 i]= i^n (0)= 0 Ans: 0 ...

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Properties of Iota

Find the valu...

Question

Find the value of $i^{n} + i^{n + 1} + i^{n + 2} + i^{n + 3}$ for all $n \in N$ .

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Solution

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If P(n) : $2 \times 4^{2 n + 1} + 3^{3 n + 1}$ is divisible by $λ$ for all $n ϵ N$ is true, then find the value of $λ$ .

ℕ

i^{n} + i^{n + 1} + i^{n + 2} + i^{n + 3}

10^{n} + 3 \times 4^{n + 1} + p

\in

$1 \times 1! + 2 \times 2! + 3 \times 3! + . . . . . + n \times n! = (n + 1)! - 1$ for all N $ϵ$ N.

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