Cheenta has planed to initiate a problem solving Marathon with existing students. Here we are providing the problems and hints of “Problem Solving Marathon Week 1“. The Set comprises three levels of questions as following-Level 0- for Class III-V; Level 1- for Class VI-VIII; Level 2- for the class IX-XII. You can post your alternative idea/solution in here.
(Q.1)Which of the following is equal to ?
Try to use the fact
(Q.2)Let and be the following sums of arithmetic sequences: What is the value of ?
Observe that how many terms are there, in and . If there are nos. of terms then pair up like term, term, term, term
If you add the elements of every pair, then you will get same result of every pair.
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(Q.1)Find all positive integers such that is divisible by .
can be written as
Try to find the necessary condition for
(Q.2)Two geometric sequences and have the same
common ratio, with , , and . Find .
Example of Geometric Sequence , here common ratio is .
Try to find the th term of geometric sequence
Analyze the example
is an example of geometric sequence. Here common ratio is . Now term . term term , term term , term term .
(Q.1)Let , , be real numbers such that .
Here you can use the idea of Cauchy Schwarz Inequality