The value of S=(5/12 ⋅ 42)+(11/42 ⋅ 72)+(17/72 ⋅ 102)+⋅s ∞ is

Question

The value of S=(5/12 ⋅ 42)+(11/42 ⋅ 72)+(17/72 ⋅ 102)+⋅s ∞ is (A) 1 (B) 1 / 2 (C) 1 / 3 (D) 1 / 4

Tardigrade Admin · Accepted Answer

S=(5/12 ⋅ 42)+(11/42 ⋅ 72)+(17/72 ⋅ 102)+⋅s ∞ 3 S=(3 ⋅ 5/12 ⋅ 42)+(3 ⋅ 11/42 ⋅ 72)+(3 ⋅ 17/72 ⋅ 102)+⋅s ∞ ⇒ 3 S=((4-1)(4+1)/12 ⋅ 42)+((7-4)(7+4)/42 ⋅ 72) +((10-7)(10+7)/72 ⋅ 102)+⋅s ∞ ⇒ S=(1/3)

Q. The value of $S = \frac{5}{1 ^{2} \cdot 4 ^{2}} + \frac{11}{4 ^{2} \cdot 7 ^{2}} + \frac{17}{7 ^{2} \cdot 1 0 ^{2}} + \dots \infty$ is

1

$1/2$

$1/3$

$1/4$

Q. The value of S=12⋅425​+42⋅7211​+72⋅10217​+⋯∞ is

1

1/2

1/3

1/4

S=12⋅425​+42⋅7211​+72⋅10217​+⋯∞ 3S=12⋅423⋅5​+42⋅723⋅11​+72⋅1023⋅17​+⋯∞ ⇒3S=12⋅42(4−1)(4+1)​+42⋅72(7−4)(7+4)​ +72⋅102(10−7)(10+7)​+⋯∞ ⇒S=31​

Q. The value of $S = \frac{5}{1 ^{2} \cdot 4 ^{2}} + \frac{11}{4 ^{2} \cdot 7 ^{2}} + \frac{17}{7 ^{2} \cdot 1 0 ^{2}} + \dots \infty$ is

$1/2$

$1/3$

$1/4$