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Q.

If I=∑k=198∫kk+1k+1x(x+1)dx , then

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a

I>4950

b

I<4950

c

I>log99 e

d

I

answer is A.

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Detailed Solution

I=∑k=198∫kk+1k+1xx+1dx=∑k=198k+1logxx+1 kk+1=2log221.3+3.log322.4+4.log423.5+.....+99log99298.100=log24.36.48.510.612−−−−−98196.991982336.48.510−−−−−98196.9998.10099             =log2.9910010099 
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