a) Số lượng số hạng:
\(\left(88-1\right):3+1=30\)(số hạng)
Giá trị của tổng là:
\(\left(88+1\right)\times30:2=1335\)
b) Cho: \(A=\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+...+\dfrac{1}{512}\)
\(\Rightarrow\dfrac{4}{2}A=\dfrac{4}{2}\times\left(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+..+\dfrac{1}{512}\right)\)
\(\Rightarrow2A=\left(1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{256}\right)\)
\(\Rightarrow2A-A=\left(1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{256}\right)-\left(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{512}\right)\)
\(\Rightarrow A=\left(\dfrac{1}{2}-\dfrac{1}{2}\right)+\left(\dfrac{1}{4}-\dfrac{1}{4}\right)+\left(\dfrac{1}{8}-\dfrac{1}{8}\right)+...+\left(\dfrac{1}{256}-\dfrac{1}{256}\right)+\left(1-\dfrac{1}{512}\right)\)
\(\Rightarrow A=0+0+0+...+\left(1-\dfrac{1}{512}\right)\)
\(\Rightarrow A=\dfrac{511}{512}\)
