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Prove that, 1/(2.3)-1/(4.5)+1/(6.7)+.......

Prove that, `1/(2.3)-1/(4.5)+1/(6.7)+.....=1-log_e2`

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MAHAVEER PUBLICATION-SERIES-QUESTION BANK
  1. Prove that, 1/(1.2)-1/(2.3)+1/(3.4)-.....=2loge2-1

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  2. Show tha, 1+1/(2!)+1/(4!)+....=1/2(e+1/e)

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  3. Prove that, 1/(2.3)-1/(4.5)+1/(6.7)+.....=1-loge2

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  4. Prove that, 1+(1+2)/(2!)+(1+2+3)/(3!)+(1+2+3+4)/(4!)+....=(3e)/2

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  5. Find the sum of odd integers from 1 to 2001.

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  6. Find 11^(th) term in 09,17,25,33,…..

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  7. How many terms of the A.P. -6,-(11)/(2),-5… are needed to give the sum...

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  8. How many terms of the series : 93+90+87+84+….. Will amount to 975 ?

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  9. Find four arithmetic mean between 3 and 23 ?

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  10. Insert two arithmetic mean between 16 and 22.

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  11. Insert three arithmetic mean (AM) between 1 and 1/16.

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  12. Insert four arithmetic mean (AM) between 4 and 19.

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  13. Insert three arithmetic mean (AM) between 6 and 18.

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  14. Is 292 a term of the A.P. series 1,4,7,10,…..? Explain.

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  15. In an A.P the 1^(st) term is 2sqrt2 and the 13^(th) term is 8sqrt2. ...

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  16. The 12^(th) term and 15^(th) term of an AP are 68 and 86 respectively....

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  17. If A.M. and GM. of two positive numbers a and b are 10 and 8, respe...

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  18. Find the sum of first n terms and the sum of first 5 terms of the geo...

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  19. Find the sum of the sequence 7, 77, 777, 7777, . . . to n terms.

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  20. How many numbers divisible by 17 are there in between 25 and 450 ?

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