Latihan Matematika Wajib Kelas XI Induksi Matematika pada Ketidaksamaan
# 6
Pilgan

Diketahui P(n) : 1+122+132+142+⋯+1n2≤2−1nP\left(n\right)\ :\ 1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\dots+\frac{1}{n^2}\le2-\frac{1}{n} untuk setiap bilangan asli nn. Diandaikan benar untuk n=kn=k, maka akan dibuktikan benar bahwa ....

A

1+122+132+142+...+1n2≤2−1k1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{n^2}\le2-\frac{1}{k}

B

1+122+132+142+...+1n2≤2−1k+11+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{n^2}\le2-\frac{1}{k+1}

C

1+122+132+142+...+1k2≤2−1k1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{k^2}\le2-\frac{1}{k}

D

1+122+132+142+...+1k2+1(k+1)2≤2−1k+11+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{k^2}+\frac{1}{\left(k+1\right)^2}\le2-\frac{1}{k+1}

E

1+122+132+142+...+1k2+1(k+1)2≤2−1k1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{k^2}+\frac{1}{\left(k+1\right)^2}\le2-\frac{1}{k}

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