AravindG
justify (5^k5) always divisible by 4



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OsmondF
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dw:1332390749082:dw

Ishaan94
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Use Induction!

NotTim
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Logs? YOu try logarthmic? WHY DID YOU ASK ME...

AravindG
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how??

Ishaan94
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Hmm
\[\frac{(1+4)^k  1  4}{4}\]
Try to use the binomial expansion, the 1 would cancel, leaving only the factors of 4.

AravindG
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srry i didnt get that

AravindG
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what to do with (1+4)^k

vishal_kothari
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dw:1332391543618:dwdw:1332391574845:dwdw:1332391595432:dwdw:1332391616609:dwdw:1332391646332:dwdw:1332391674792:dw

Ishaan94
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Use the binomial expansion
\[(1+4)^k = \underbrace{\binom{k}{0}4^{0}1^{k}}_{\text{This is 1}} + \binom{k}{1}4^1 1^{k1} + \ldots + \binom{k}{k}4^k \]
\[\frac{1 + \binom{k}{1}4^1 1^{k1} + \ldots + \binom{k}{k}4^k 1 4}{4}\]

AravindG
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oh k thx evryone