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Question Number 202324 by hardmath last updated on 24/Dec/23

Find : \frac{\frac{1}{2} + 1 + \frac{3}{2} + \dots + 16}{\frac{1}{4} + \frac{2}{4} + \frac{3}{4} + \dots + 8}

Answered by MATHEMATICSAM last updated on 24/Dec/23

\frac{\frac{1}{2} + 1 + \frac{3}{2} + \dots . + 16}{\frac{1}{4} + \frac{2}{4} + \frac{3}{4} + \dots . + 8}

= \frac{\frac{1}{2} + \frac{2}{2} + \frac{3}{2} + \frac{4}{2} + \dots . + \frac{32}{2}}{\frac{1}{4} + \frac{2}{4} + \frac{3}{4} + \frac{4}{4} + \dots . + \frac{32}{4}}

= \frac{\frac{1}{2} [1 + 2 + 3 + 4 + \dots . + 32]}{\frac{1}{4} [1 + 2 + 3 + 4 + \dots . + 32]}

= \frac{1}{2} \times 4

= 2

Commented by hardmath last updated on 24/Dec/23

thankyou dear professor /

Answered by Rasheed.Sindhi last updated on 25/Dec/23

\frac{\frac{1}{2} + 1 + \frac{3}{2} + \dots + 16}{\frac{1}{4} + \frac{2}{4} + \frac{3}{4} + \dots + 8}

I n o r d e r t o k i l l t h e d e n o m i n a t o r s

m u l t i p l y n u m e r a t o r & d e n o m i n a t o r b y 4

= \frac{4 (\frac{1}{2} + 1 + \frac{3}{2} + \dots + 16)}{4 (\frac{1}{4} + \frac{2}{4} + \frac{3}{4} + \dots + 8)}

= \frac{2 (1 + 2 + 3 + \dots + 32)}{(1 + 2 + 3 + \dots + 32)} = 2

Commented by MathematicalUser2357 last updated on 26/Dec/23

denominators {isn}^{'} t humans

Commented by Rasheed.Sindhi last updated on 26/Dec/23