Sequence And Series Question 494
Question: A series whose nth term is $ ( \frac{n}{x} )+y, $ the sum of r terms will be
[UPSEAT 1999]
Options:
A) $ { \frac{r(r+1)}{2x} }+ry $
B) $ { \frac{r(r-1)}{2x} } $
C) $ { \frac{r(r-1)}{2x} }-ry $
D) $ { \frac{r(r+1)}{2y} }-rx $
Show Answer
Answer:
Correct Answer: A
Solution:
On putting $ n=1,2,3,….. $ First term of the series $ a=\frac{1}{x}+y $ , Second term = $ \frac{2}{x}+y $ \ $ d=( \frac{2}{x}+y )-( \frac{1}{x}+y )=\frac{1}{x} $ Sum of $ r $ terms of the series $ =\frac{r}{2}[ 2( \frac{1}{x}+y )+(r-1)\frac{1}{x} ] $ $ =\frac{r}{2}[ \frac{2}{x}+2y+\frac{r}{x}-\frac{1}{x} ] $ $ =\frac{r^{2}-r+2r}{2x}+ry=[ \frac{r,(r+1)}{2x}+ry ] $ .
BETA
