Let k be an integer. When can we claim the following?k2 =kXi=1kExperiment with that expression for several values of k before answer-ing the question.
Question
Let k be an integer. When can we claim the following?
k^2 = k \sum_{i=1}^{k} k
Experiment with that expression for several values of k before answering the question.
Solution
The question seems to be asking when the equation k^2 = k * Σi=1 to k is true, where k is an integer.
The symbol Σ from i=1 to k is the sum of all integers from 1 to k. This is a well-known formula and it equals to k*(k+1)/2.
So, the equation becomes k^2 = k * k*(k+1)/2.
Simplify the equation, we get 2k = k+1.
Solving for k, we get k = 1.
So, the equation is true when k is 1.
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