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How To Start Learning


Happy Learning 

Hello students , 
Welcome to How to start Learning - we are very happy to meet you here. You are joining one of the famous popular blog in the world. 

  • Start again if you ever get stuck 
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  • Take your test Regularly 
  • Set the goal and let mind help you in the journey

Time To Begin!

When you will finish reading our blog, you will know many techniques of learning used by experts in music, arts ,Math , Science, literature, Sports, athletic, dance and other fields. If you wanna become expert in any field this blog will help you as your guide. 
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Have lots of Fun and Happy Learning journey my friends. 


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Fibonacci Sequence Problem set 1

 Problems  1. The Fibonacci numbers can be extended to zero and negative indices using the relation Fn = Fn+2 − Fn+1 . Determine F0 and find a general formula for F−n in terms of Fn. Prove your result using mathematical induction. Solution: F0 = F2 − F1 = 0, F−1 = F1 − F0 = 1, F−2 = F0 − F−1 = −1, F−3 = F−1 − F−2 = 2, F−4 = F−2 − F−3 = −3, F−5 = F−3 − F−4 = 5, F−6 = F−4 − F−5 = −8. The correct relation appears to be F−n = (−1)^(n+1)×Fn                .............(1) We now prove equation (1) by mathematical induction. Base case: Our calculation above already shows that equation (1) is true for n = 1 and n = 2, that is, F−1 = F1 and F−2 = −F2. Induction step: Let us  assume that (1) is true for positive integers n = k − 1 and n = k. Then we have F−(k+1) = F−(k−1) − F(−k)     ..(from definition)                = (−1)^k×Fk−1 − (−1)^(k+1)×Fk           ...

Fibonacci Sequence and Climbing Staircase problem

Hello Friends, So here is our next blog on Fibonacci  Sequence. In this blog I will introduce another problem whose solution is the Fibonacci Number. This problem is known as Climbing Staircase problem. The Question is How many ways one can climb staircase with n steps, taking one or two steps at a time ?? Questions Of Climbing Staircase  Eg. Suppose we have 3 steps to climb. So we have a Staircase, we climb it by taking one step , one step , one step or two step , one step or one step, two step. So If we have n-steps in Staircase , then how many different ways can we climb the Staircase? So to answer this question we could make a table, considering small numbers of steps i.e n = 1,2,3,4,5 And we can list the number of ways to climb the Staircase. So Observe the table first column is number of stairs or steps. Second column is the list of ways one can climb by taking one or two steps at a time. Third column a n   the total number of ways to climb Staircase. I hope y...

Humans-puppet of mobile phones Part-1

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