infinite


Calculate Sum of Infinite Numbers Series [closed]


Given is number series
-3/2 + 3/4 - 3/8 + 3/16 Sum of Infinite Series equal to?
Elaborate with steps please.
Cannot find the solution
You know you can't calculate infinite cycle in programming. But you can calculate approximate result. For example if (result_i -result_i+1) < 0.00001 so you can have some pseudo code.
double difference = 1;
double sum = 0;
long divideValue = 2;
int plusOrMinus = -1;
while(difference > 0.00001) {
double oldSum = sum;
sum += plusOrMinus * (-3/divideValue);
plusOrMinus *= -1;
divideValue *=2;
difference = sum - oldSum;
}
Well, S = 1 - 1/2 + 1/4 - 1/8 ... = ln(2)
Therefore, -3/2 + 3/4 - 3/8 ... = 3 * S - 3 = 3 * ln(2) - 3

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