JEE-Level Application Problems

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Try the first 5 questions

1.
4^n-3n-1 is divisible by 9 for all n>=1. In the inductive step, 4^(k+1)-3(k+1)-1 equals:
2.
sum(1/(sqrt(k)+sqrt(k+1)), k=1 to 24) =
3.
sum(arctan(1/(2k^2)), k=1 to 5) =
4.
If S_n = sum(k^2, k=1 to n) and S_20 - S_10 =?
5.
sum(k/(k+1)!, k=1 to 20) =

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