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Sequences and Series question

2020 · 3 Sep · Shift 1 · Q40
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Sequences and Series question

2020 · 3 Sep · Shift 1 · Q40

JEE MainMathematicsSequences and SeriesNumerical+4 / −1
The value of (0.16)log⁡2.5(13+132+....to ∞){\left( {0.16} \right)^{{{\log }_{2.5}}\left( {{1 \over 3} + {1 \over {{3^2}}} + ....to\,\infty } \right)}}(0.16)log2.5​(31​+321​+....to∞) is equal to ‾\underline{\hspace{2cm}}​.
Numerical answer
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