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Question : 18 of 160
Marks:
+1,
-0
Solution:
It is given that
x=‌+‌+‌+... So x=‌+‌+‌| 3⋅5⋅7⋅9 |
| 5â‹…10â‹…15â‹…20 |
+... The general term is
Tr+1‌‌=‌| 3⋅5⋅7...(2r+1) |
| 5râ‹…1â‹…2â‹…3...r |
=(‌)r‌ =‌| (−)(−−1)(−−2)...(−−r+1)(−)r |
| r! |
Compare above with general terms of expansion
(1+x)n ‌| n(n−1)(n−2)...(n−r+1)xr |
| r! |
This gives,
n=−‌,x=−‌ Then,
x+‌‌‌=(1−‌)−‌ ‌‌=(‌)−‌ ‌‌=(‌)‌ ‌‌=‌ So,
‌‌‌=‌ 5x+8‌‌=‌
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