MathDB

4

Part of 1984 National High School Mathematics League

Problems(2)

The Number of Real Roots

Source: 1984 National High School Mathematics League, Exam One, Problem 4

2/22/2020
The number of real roots of the equation sin⁡x=lg⁡x\sin x=\lg x is (A)1(B)2(C)3(D)\text{(A)}1\qquad\text{(B)}2\qquad\text{(C)}3\qquad\text{(D)}more than 33
Complete Alternation

Source: 1984 National High School Mathematics League, Exam Two, Problem 4

2/22/2020
Define ana_n: the last digit of 12+22+32+⋯+n21^2+2^2+3^2+\cdots+n^2. Prove that 0.a1a2a3⋯‾\overline{0.a_1 a_2 a_3 \cdots} is a rational number.