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3. if na=1 al...

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3. if na=1 always and n goes to infinite, then the value of

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Q. If n is any natural number, then 6ⁿ − 5ⁿ always ends with

(a) 1
(b) 3
(c) 5
(d) 7

[Hint: For any n ∈ N, 6ⁿ and 5ⁿ end with 6 and 5 respectively. Therefore, 6ⁿ − 5ⁿ always ends with 6 − 5 = 1.]

S_{\infty} = \frac{1}{1 \cdot 3 \cdot 5} + \frac{1}{3 \cdot 5 \cdot 7} + \frac{1}{5 \cdot 7 \cdot 9} + \dots

up to infinite term, then the value of

24 S_{\infty}

S_{\infty} = \frac{1}{1 \cdot 3 \cdot 5} + \frac{1}{3 \cdot 5 \cdot 7} + \frac{1}{5 \cdot 7 \cdot 9} + \dots

up to infinite term, then the value of

24 S_{\infty}

a < c

Δ A B C,

then sum to infinite terms of the series

n \frac{a}{c} sin B + \frac{n (n + 1)}{2!} \frac{a^{2}}{c^{2}} sin 2 B + . . . . . \infty

Q. If an electron of an atom goes from

n = 1

n = 3

then its time period become _______ times of the initial value.

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