(1/2.5)+(1/5.8)+(1/8.11)+ ldots 16 terms =

Question

(1/2.5)+(1/5.8)+(1/8.11)+ ldots 16 terms = (A) (4/25) (B) (8/25) (C) (16/25) (D) (1/25)

Tardigrade Admin · Accepted Answer

Given, (1/2 ⋅ 5) +(1/5 ⋅ 8)+(1/8 ⋅ 11)+ ldots .16 terms =(1/3)[(3/2 ⋅ 5)+(3/5 ⋅ 8)+(3/8 ⋅ 11)+ ldots .] =(1/3)[(1/2)-(1/5)+(1/5)-(1/8)+(1/5)-(1/11)+ ldots .+(1/47)-(1/50)] =(1/3)[(1/2)-(1/50)]=(1/3)[(48/100)]=(1/3)[(24/50)]=(8/50)=(4/25)

Q. $\frac{1}{2.5} + \frac{1}{5.8} + \frac{1}{8.11} + \dots 16$ terms $=$

$\frac{4}{25}$

$\frac{8}{25}$

$\frac{16}{25}$

$\frac{1}{25}$

Q. 2.51​+5.81​+8.111​+…16 terms =

254​

258​

2516​

251​

Given, 2⋅51​+5⋅81​+8⋅111​+….16 terms =31​[2⋅53​+5⋅83​+8⋅113​+….] =31​[21​−51​+51​−81​+51​−111​+….+471​−501​] =31​[21​−501​]=31​[10048​]=31​[5024​]=508​=254​

Q. $\frac{1}{2.5} + \frac{1}{5.8} + \frac{1}{8.11} + \dots 16$ terms $=$

$\frac{4}{25}$

$\frac{8}{25}$

$\frac{16}{25}$

$\frac{1}{25}$