Tính nhanh
S = $\frac{1}{3}$ + $\frac{1}{3^2}$ + $\frac{1}{3^4}$ +… + $\frac{1}{3^86}$
Tính nhanh S = $\frac{1}{3}$ + $\frac{1}{3^2}$ + $\frac{1}{3^4}$ +… + $\frac{1}{3^86}$
By Adalynn
By Adalynn
Tính nhanh
S = $\frac{1}{3}$ + $\frac{1}{3^2}$ + $\frac{1}{3^4}$ +… + $\frac{1}{3^86}$
Giải thích các bước giải:
S = 13+132+134+..+138613+132+134+..+1386
=> 3232S = 9S = 3+1+132+….+13843+1+132+….+1384
=> 8S = 4−13−13864-13-1386 = 113−1386113-1386
=> S = 113−13868
S = `1/3+1/3^2+1/3^4+..+1/3^86`
=> `3^2`S = 9S = `3 + 1 + 1/3^2 + ….+1/3^84`
=> 8S = `4 – 1/3 – 1/3^86` = `11/3 – 1/3^86`
=> S = `(11/3 – 1/3^86)/8`