Question

Class XI... No spamming ​

Answer 1

$Given \: \: Question \: \: Is \: \: \\ \\ To \: \: prove \: \\ \\ \frac{(3 {}^{k} - 1)}{2} + 3 {}^{k} = \frac{(3 {}^{(k + 1)} - 1) }{2} \\ \\ Answers \: \\ \\ l.h.s \\ \\ \frac{(3 {}^{k} - 1)}{2} + 3 {}^{k} \\ \\ \frac{(3 {}^{k} - 1) + 3 {}^{k} \times 2}{2} \\ \\ \frac{(3 \times 3 {}^{k}) - 1}{2} \\( becoz \: \: 2 \times \alpha + \alpha = 3 \alpha ) \\ \\ \frac{(3 {}^{(k + 1)} - 1)}{2} \\ \\ therefore \: \: \\ \frac{(3 {}^{k} - 1)}{2} + 3 {}^{k} = \frac{(3 {}^{(k + 1)} - 1) }{2} \\ hence \: \: l.h.s = r.h.s$