Welcome to the article Evaluate tex sum r 3 7 2 r tex A 324 B 224 C 248 D 313. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!
Answer :
We want to evaluate
$$
\sum_{r=3}^7 2^r = 2^3 + 2^4 + 2^5 + 2^6 + 2^7.
$$
Step 1: Evaluate each term:
- For $r=3$, we have $2^3 = 8$.
- For $r=4$, we have $2^4 = 16$.
- For $r=5$, we have $2^5 = 32$.
- For $r=6$, we have $2^6 = 64$.
- For $r=7$, we have $2^7 = 128$.
Step 2: Sum all the computed terms:
$$
8 + 16 = 24,
$$
$$
24 + 32 = 56,
$$
$$
56 + 64 = 120,
$$
$$
120 + 128 = 248.
$$
Thus, the value of the sum is
$$
\boxed{248}.
$$
$$
\sum_{r=3}^7 2^r = 2^3 + 2^4 + 2^5 + 2^6 + 2^7.
$$
Step 1: Evaluate each term:
- For $r=3$, we have $2^3 = 8$.
- For $r=4$, we have $2^4 = 16$.
- For $r=5$, we have $2^5 = 32$.
- For $r=6$, we have $2^6 = 64$.
- For $r=7$, we have $2^7 = 128$.
Step 2: Sum all the computed terms:
$$
8 + 16 = 24,
$$
$$
24 + 32 = 56,
$$
$$
56 + 64 = 120,
$$
$$
120 + 128 = 248.
$$
Thus, the value of the sum is
$$
\boxed{248}.
$$
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Rewritten by : Brahmana