Question

Tính:

S₁:(1/2-1)x(1/3-1)x(1/4-1)x..............x(1/100-1)

S₂:3/2²x8/3²x10/4²x...............x899/30²

S₃:5⁵+5⁶+...............+5¹⁰⁰

S₄:7/10x11+7/11x12+.................+7/69x70

S₅:15/90x95+15/94x98+.....................+15/146x150

S_6:10/56+10/140+10/28+...................+10/1400

gs mk nhé !
 

Answer 1

a: \(S=\dfrac{-1}{2}\cdot\dfrac{-2}{3}\cdot...\cdot\dfrac{-99}{100}=-\dfrac{1}{100}\)

c: \(5S_3=5^6+5^7+...+5^{101}\)

\(\Leftrightarrow4\cdot S_3=5^{101}-5^5\)

hay \(S_3=\dfrac{5^{101}-5^5}{4}\)

d: \(S_4=7\cdot\left(\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}+...+\dfrac{1}{69}-\dfrac{1}{70}\right)\)

\(=7\left(\dfrac{1}{10}-\dfrac{1}{70}\right)=7\cdot\dfrac{6}{70}=\dfrac{6}{10}=\dfrac{3}{5}\)