Question

1/2+2/3+3/4+4/5+.......+ 49/50咋个算?

Answer 1

1/2+2/3+3/4+4/5+.......+
49/50
=1-1/2+(1-1/3)+(1-1/4)+..+(1-1/50)
=50-(1+1/2+1/3+1/4+..+1/50)
1+1/2+1/3+......+1/n≈lnn+C(C=0.57722......一个无理数,称作欧拉初始,专为调和级数所用)
1+1/2+1/3+1/4+..+1/50=ln50+0.577=3.912+0.577=4.489