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Question : 18 of 160
Marks:
+1,
-0
Solution:
We have,
1−‌+‌(‌)2−‌(‌)3+...= We know that,
(1−x)n=1−nx+‌x2−‌x3 Let
(1−x)n=1−‌+‌(‌)2−‌(‌)3⋅s ∴‌‌nx=‌ and
‌x2=‌(‌)2 nx=‌ and
n(n−1)x2=4(‌)2 n2⋅x2=‌ and
n(n−1)x2=4(‌)2 n(n−1)x2=4n2x2 n2−n=4n2 .n−1=4n⇒n=−‌ x=‌×−3=‌ (1−x)n=(1+‌)−1∕3=(‌)−1∕3=(‌)2∕3
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