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Beyond Horizon Set 3 Paper 2 · Q15

Paper 2Calculus

Find an expression for ∫1n(−1)⌊x⌋⌊x⌋−1 dx\displaystyle\int_1^n(-1)^{\lfloor x\rfloor}\lfloor x\rfloor^{-1}\,dx where n∈Nn\in\mathbb{N}.

A∑k=1n(−1)k1k\displaystyle\sum_{k=1}^n(-1)^k\frac1k
B∑k=1n−1(−1)k1k\displaystyle\sum_{k=1}^{n-1}(-1)^k\frac1k
C∑k=1n−1(−1)k1k2\displaystyle\sum_{k=1}^{n-1}(-1)^k\frac1{k^2}
D∑k=1n(−1)k1k2\displaystyle\sum_{k=1}^n(-1)^k\frac1{k^2}

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