Determine how many terms are needed in the series klog k 1

Determine how many terms are needed in the series k(log (k + 1)), where k = 1, 2..., to make the sum of the terms exceeds quantity 10,000. In other words, determine the smallest N, for the following sum, such that the sum becomes greater or equal to 10,000 sigma_k = 1^N k log (k + 1).

Solution

sum =0;
k=0;
while sum<10000
k=k+1;
sum = sum+k*log10(k+1);%taking the sum
end
disp(k);
disp(sum);

output:

105

1.0096e+004

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