Harish Kayarohanam
Reputation
1,662
Next privilege 2,000 Rep.
5 18
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~44k people reached

 9 Find the value of $3^9\cdot 3^3\cdot 3\cdot 3^{1/3}\cdot\cdots$ 8 Prove that $\log_{36} 30$ is irrational number. 7 Show that $\sin2\alpha\cos\alpha+\cos2\alpha\sin\alpha = \sin4\alpha\cos\alpha - \cos4\alpha\sin\alpha$ 6 If $2^x=3^y=6^{-z}$ then prove that:$\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0$ 6 Is there a simpler way to express the fraction $\frac{x}{x+y}$?

### Reputation (1,662)

 +10 $5^{2012}+1$ is divisible with $313$ +10 Prove that $\log_{36} 30$ is irrational number. +10 In how many ways can a number be expressed as a sum of consecutive numbers? +5 what is the default order and direction of operation?

### Questions (15)

 8 Why is the Fibonacci ratio though a decreasing function, it is alternating and decreasing? 4 How to find in which number base the operation was done by looking at the corresponding operation in decimal system? 4 summation of consecutive natural numbers does not end in 7,4,2,9 4 On comparing fractions , fraction with smaller difference between numerator and denominator is greater than the other 3 Find time when 2 cars meet?

### Tags (50)

 27 algebra-precalculus × 15 9 infinite-product 17 geometry × 14 9 recreational-mathematics 15 number-theory × 11 9 problem-solving 13 elementary-number-theory × 12 8 trigonometry × 2 9 combinatorics × 11 6 permutations × 8

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