JEE PYQ: Sequence And Series Question 50
Question 50 - 2019 (09 Apr Shift 2)
The sum of the series $1 + 2 \times 3 + 3 \times 5 + 4 \times 7 + \ldots$ upto $11^{th}$ term is:
(1) 915
(2) 946
(3) 945
(4) 916
Show Answer
Answer: (2)
Solution
$1 + 2.3 + 3.5 + 4.7 + \ldots$
Let $S = (2.3 + 3.5 + 4.7 + \ldots)$
Now, $S_{10} = \sum_{n=1}^{10}(n+1)(2n+1) = \sum_{n=1}^{10}(2n^2 + 3n + 1)$
$= \frac{2.10.11.21}{6} + \frac{3.10.11}{2} + 10 = 945$
Hence required sum of the series $= 1 + 945 = 946$
BETA
