Sum of the series (1/1.2)-(1/2.3)+(1/3.4)-(1/4.5)+.... is

Question

Sum of the series (1/1.2)-(1/2.3)+(1/3.4)-(1/4.5)+.... is (A)  log text 2  (B)  log text 3  (C)  2 text log text 2-1  (D)  2 text log text 3-1

Tardigrade Admin · Accepted Answer

Given, (1/1.2)-(1/2.3)+(1/3.4)-(1/4.5)+.... =( 1-(1/2) )-( (1/2)-(1/3) )+( (1/3)-(1/4) )... =1-2.(1/2)+2.(1/3)-2.(1/4)+....-1+1 =2[ 1-(1/2)+(1/3)-(1/4)+..... ]-1 =2 text log(1+1)-1 =2 text log text 2-1

Q. Sum of the series $\frac{1}{1.2} - \frac{1}{2.3} + \frac{1}{3.4} - \frac{1}{4.5} + ....$ is

$l o g 2$

$l o g 3$

$2 l o g 2 - 1$

$2 l o g 3 - 1$

Q. Sum of the series 1.21​−2.31​+3.41​−4.51​+.... is

log2

log3

2log2−1

2log3−1

Given, 1.21​−2.31​+3.41​−4.51​+.... =(1−21​)−(21​−31​)+(31​−41​)... =1−2.21​+2.31​−2.41​+....−1+1 =2[1−21​+31​−41​+.....]−1 =2log(1+1)−1 =2log2−1

Q. Sum of the series $\frac{1}{1.2} - \frac{1}{2.3} + \frac{1}{3.4} - \frac{1}{4.5} + ....$ is

$l o g 2$

$l o g 3$

$2 l o g 2 - 1$

$2 l o g 3 - 1$