91Ó°ÊÓ

State whether the given sums are equal or unequal. $$a\sum_{i=1}^{10} i and \sum_{k=1}^{10} k$$ $$b. \sum_{i=1}^{10} i and \sum_{i=6}^{15}(i-5)$$ $$c. \sum_{i=1}^{10} i(i-1) and \sum_{j=0}^{9}(j+1) j$$ $$d. \sum_{i=1}^{10} i(i-1) \text { and } \sum_{k=1}^{10}\left(k^{2}-k\right)$$

In the following exercises, use the rules for sums of powers of integers to compute the sums. \(\sum_{i=5}^{10} i\)

In the following exercises, use the rules for sums of powers of integers to compute the sums. $$\sum_{i=5}^{10} i^{2}$$

Suppose that \(\sum_{i=1}^{100} a_{i}=15\) and \(\sum_{i=1}^{100} b_{i}=-12 .\) In the following exercises, compute the sums. $$\sum_{i=1}^{100}\left(a_{i}+b_{i}\right) $$

Suppose that \(\sum_{i=1}^{100} a_{i}=15\) and \(\sum_{i=1}^{100} b_{i}=-12 .\) In the following exercises, compute the sums. $$\sum_{i=1}^{100}\left(a_{i}-b_{i}\right)$$

Suppose that \(\sum_{i=1}^{100} a_{i}=15\) and \(\sum_{i=1}^{100} b_{i}=-12 .\) In the following exercises, compute the sums. $$\sum_{i=1}^{100}\left(3 a_{i}-4 b_{i}\right)$$

Suppose that \(\sum_{i=1}^{100} a_{i}=15\) and \(\sum_{i=1}^{100} b_{i}=-12 .\) In the following exercises, compute the sums. $$\sum_{i=1}^{100}\left(5 a_{i}+4 b_{i}\right)$$

In the following exercises, use summation properties and formulas to rewrite and evaluate the sums. $$\sum_{k=1}^{20} 100\left(k^{2}-5 k+1\right)$$

In the following exercises, use summation properties and formulas to rewrite and evaluate the sums. $$\sum_{j=1}^{50}\left(j^{2}-2 j\right)$$

In the following exercises, use summation properties and formulas to rewrite and evaluate the sums. $$\sum_{j=11}^{20}\left(j^{2}-10 j\right)$$