The sum of the series (5/12 ⋅ 42)+(11/42 ⋅ 72)+(17/72 ⋅ 102)+. ldots ldots . is

Question

The sum of the series (5/12 ⋅ 42)+(11/42 ⋅ 72)+(17/72 ⋅ 102)+. ldots ldots . is (A) (1/2) (B) (1/3) (C) 2 (D) 3

Tardigrade Admin · Accepted Answer

S=(5/12 ⋅ 42)+(11/42 ⋅ 72)+(17/72 ⋅ 102)+. ldots 3S=(3.5/12 ⋅ 42)+(3 ⋅ 11/42 ⋅ 72)+(3 ⋅ 17/72 ⋅ 102)+. ldots . 3S=((4 - 1) (4 + 1)/12 ⋅ 42)+((7 - 4) (7 + 4)/42 ⋅ 72)+((10 - 7) (10 + 7)/72 ⋅ (10)2)+. ldots . 3S=(42 - 12/12 ⋅ 42)+(72 - 42/42 ⋅ 72)+(102 - 72/72 ⋅ 102)+. ldots . =(1/12)-(1/42)+(1/42)-(1/72)+(1/72)-(1/102)+. ldots . ⇒ 3S=1 S=(1/3)

Q. The sum of the series $\frac{5}{1 ^{2} \cdot 4 ^{2}} + \frac{11}{4 ^{2} \cdot 7 ^{2}} + \frac{17}{7 ^{2} \cdot 1 0 ^{2}} + . \dots\dots .$ is

$\frac{1}{2}$

$\frac{1}{3}$

$2$

$3$

Q. The sum of the series 12⋅425​+42⋅7211​+72⋅10217​+.……. is

21​

31​

2

3

Q. The sum of the series $\frac{5}{1 ^{2} \cdot 4 ^{2}} + \frac{11}{4 ^{2} \cdot 7 ^{2}} + \frac{17}{7 ^{2} \cdot 1 0 ^{2}} + . \dots\dots .$ is

$\frac{1}{2}$

$\frac{1}{3}$

$2$

$3$