Question

tính tổng s=3+3/2+3/2^2+...+3/2^9

Answer 1

S = 3 + \(\frac32\) + \(\frac{3}{2^2}\) + ... + \(\frac{3}{2^9}\)

S x 2 = 6 + \(\) 3 + \(\frac32\) +... + \(\frac{3}{9^8}\)

S x 2 - S = 6 + \(\) 3 + \(\frac32\) +... + \(\frac{3}{2^8}\) - 3 - \(\frac32\) - \(\frac32\) - ... - \(\frac{3}{2^8}\) - \(\frac{3}{2^8}\)

S = (6 - \(\frac{3}{2^9}\)) + (3 -3) + (\(\frac32\) - \(\frac32\)) + ... + (\(\frac{3}{2^8}\) - \(\frac{3}{2^8}\))

S = 6 - \(\frac{3}{2^9}\)