G.P?

Let $f(1)=1$ and $\displaystyle f(n)=2\sum_{r=1}^{n-1}f(r)$ . Then find $\large \sum_{n=1}^{m}f(n)$

#Algebra

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Answer is 3^(m-1)

Aaghaz Mahajan - 2 years, 8 months ago

Correct answer...

Vilakshan Gupta - 2 years, 8 months ago

@Vilakshan Gupta Slack check kara tune??? Maine voh quadratic waale question ka answer bhej diya hai...........

Aaghaz Mahajan - 2 years, 8 months ago

Simply observe the pattern and prove by induction that
f(n) = 2*3^(n-2) for all n>=2 !!!!

Aaghaz Mahajan - 2 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$