JEE Mains · Maths · STD 11 - 8. sequence and series
If the sum of the first 10 terms of the series \(\frac{4.1}{1+4.1^4}+\frac{4.2}{1+4.2^4}+\frac{4.3}{1+4.3^4}+\ldots\) is \(\frac{m}{n}\), where \(\operatorname{gcd}(m, n)=1\), then \(m+n\) is equal to______
- A 440
- B 441
- C 442
- D 443
Answer & Solution
Correct Answer
(B) 441
Step-by-step Solution
Detailed explanation
\begin{aligned} & \mathrm{T}_{\mathrm{r}}=\frac{4 . \mathrm{r}}{1+4 . \mathrm{r}^4} \\ & \mathrm{~T}_{\mathrm{r}}=\frac{4 . \mathrm{r}}{\left(2 \mathrm{r}^2+2 \mathrm{r}+1\right)\left(2 \mathrm{r}^2-2 \mathrm{r}+1\right)} \\ & \mathrm{T}_{\mathrm{r}}=\frac{\left(2 \mathrm{r}^2+2…
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