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Q.

Sum of the series ∑k=1∞ ∑r=0k 22r7k kCr is

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a

17

b

47

c

2.5

d

5.2

answer is C.

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Detailed Solution

∑r=0k 22r7k kCr=17k∑r=0k kCr4r =17k(1+4)k=57kThus, ∑k=1∞ ∑r=0k 22r7k kCr =∑k=1∞ 57k=5/71−5/7=2.5

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