whether the given equation $1^{n} + 2^{n} + 3^{n} + . . . . . + 15^{n}$ is divisible by $480$ for all odd $n \geq 5$ . is ?

True

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

False

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A True
undefined

Suggest Corrections

Similar questions

ϵ

3 \times 5^{2 n + 1} + 2^{3 n + 1}

(1 + x)^{n} = n \sum r = 0^{n} C_{r} x^{n},

\frac{C_{0}}{1 \cdot 2} 2^{2} + \frac{C_{1}}{2 \cdot 3} 2^{3} + \frac{C_{2}}{3 \cdot 4} 2^{4} + \dots + \frac{C_{n}}{(n + 1) (n + 2)} 2^{n + 2}

2^{2 n} - 3 n - 1

9

n

Prove by using the principle of mathematical induction $\forall n \in N$

$2 + 5 + 8 + 11 + . . . + (3 n - 1) = \frac{1}{2} n (3 n + 1)$

Using principle of mathematical induction, prove that $4^{n} + 15 n - 1$ is divisible by 9 for all natural numbers n.

For all natural numbers n, (n+1)(n+2)(n+3) is divisible by

Join BYJU'S Learning Program