Maths · Arithmetic and Geometric progressions
Sum of nine terms of the series
Sum of nine terms of the series \( \log a+ \) \( \log \frac{a^{2}}{b}+\log \frac{a^{3}}{b^{2}}+\log \frac{a^{4}}{b^{3}}+\ldots . . i s- \)
- A. \( 36 \log a-28 \log b \)
- B. \( 45 \log a-36 \log b \)
- C. \( 55 \log a-45 \log b \)
- D. \( 66 \log a-55 \log b \)
Step-by-step solution
Each term simplifies to n log a - (n-1) log b for n=1 to 9. Sum of n from 1 to 9 is 45, sum of (n-1) from 1 to 9 is 36, giving total 45 log a - 36 log b.
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