Home › JEE Main › mathematics › Sequences and Series › The sum of the infinite GP $1 + 1/3 + 1/9 + 1/27…
The sum of the infinite GP $1 + 1/3 + 1/9 + 1/27 + \cdots$ is:
A$3/2$, since $S_\infty = a/(1 - r) = 1/(1 - 1/3) = 3/2$
B$2/3$, the inverse ratio computed wrong on the chart
C$3$, the first plus the second term simply summed
D$1$, equal to the first term of the infinite series
Answer & Solution
Correct answer: A. $3/2$, since $S_\infty = a/(1 - r) = 1/(1 - 1/3) = 3/2$
$S_\infty = 1/(1 - 1/3) = 3/2$.
Related questions
Sum of GP: 1 + 1/2 + 1/4 + ... to infinity =GP with first term 2, common ratio 3. Find 5th term.Sum of first 20 natural numbers:The 10th term of the AP 3, 7, 11, ... is:The AM-GM INEQUALITY for two POSITIVE numbers $a$ and $b$ states thatIf the AM and GM of two positive numbers are $5$ and $4$ respectively, the numbers areThree numbers are in AP. Their sum is $24$ and their product is $440$. Find the smallest oSum of the CUBES of the first $n$ natural numbers, $1^3 + 2^3 + \ldots + n^3$, equals