Let α=1/4+1/8+1/16+ ∞ and β=1/3+1/9+1/27+ ∞. Then the value of (0.2)^ log 5 (α)+(0.04)^(log ₅(β)) is equal to:

Sequence and Series: JEE Main 2026 Mathematics question

JEE Main 2026 · 4 Apr, Evening shift · Q7

JEE Main 20264 Apr, Evening shiftMathematicsEasySequence and Series179× since 2002

Let

\alpha=\frac14+\frac18+\frac1{16}+\dots\infty

and

\beta=\frac13+\frac19+\frac1{27}+\dots\infty

. Then the value of

(0.2)^{\log_{\sqrt5}(\alpha)}+(0.04)^{\log_5(\beta)}

is equal to:

JEE Main 2026 · 4 Apr, Evening shift · Q7

JEE Main 20264 Apr, Evening shiftMathematicsEasySequence and Series179× since 2002

Let

\alpha=\frac14+\frac18+\frac1{16}+\dots\infty

and

\beta=\frac13+\frac19+\frac1{27}+\dots\infty

. Then the value of

(0.2)^{\log_{\sqrt5}(\alpha)}+(0.04)^{\log_5(\beta)}

is equal to: