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Question : 92 of 150
Marks:
+1 ,
-0
Solution:
Let S = 1 + 2. 2 + 3.
2 2 +4.
2 2 + .... + 100 .
2 99 ....(i)
It is an arithmetico - geometric series.
On multiplying Eq. (i) by 2 and then subtracting it from Eq. (i), we get
S = 1 + 2.2 + 3 . 2 2 2 3 2 99 2 2 2 3 2 99 2 100 2 2 + 2 3 2 99 − 100.2 100
⇒ - S =
- 100 .
2 100 ⇒ - S =
2 100 - 1 -
100 . 2 100 ⇒ - S = - 1 - 99 .
2 100 ⇒ S = 99 .
2 100 + 1
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