JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Application +4 | -1

Let

a=2^{\frac{1}{50}}-1

and for each

n \geq 2, S_n=C_1+C_2 \cdot a+C_3 \cdot a^2+\ldots \ldots+C_n \cdot a^{n-1}

\left({ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}=\mathrm{C}_{\mathrm{r}}\right)

the

S_{101}-S_{100}=

View answer and explanation

Correct option: A

Option A (4) is correct because the expression

S_{101} - S_{100}

simplifies to 4 using the given information and binomial theorem.

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